US Army Corps of Engineers Se Nani @s Be. Leech = | LS tug Ros Gr Te a TECHNICAL REPORT CERC-86-4 REGIONAL COASTAL PROCESSES NUMERICAL MODELING SYSTEM Report 1 RCPWAVE—A LINEAR WAVE PROPAGATION MODEL FOR ENGINEERING USE by Bruce A. Ebersole, Mary A. Cialone, Mark D. Prater Coastal Engineering Research Center DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers PO Box 631, Vicksburg, Mississippi 39180-0631 March 1986 Report 1 of a Series Approved For Public Release; Distribution Unlimited : Prepared for DEPARTMENT OF THE ARMY US Army Corps of Engineers Washington, DC 20314-1000 Destroy this report when no longer needed. Do not return it to the originator. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. 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Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. il ny 0 0301 0091251 5 MI Unclassified SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE EAP NE TRUCTIONS BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO.| 3. RECIPIENT'S CATALOG NUMBER Technical Report CERC-86-4 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED REGIONAL COASTAL PROCESSES NUMERICAL MODELING AO oa Ra SYSTEM; Report 1: RCPWAVE--A LINEAR WAVE gir ra pau sesh che echt PROPAGATION MODEL FOR ENGINEERING USE 6. PERFORMING ORG. REPORT NUMBER 7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s) Bruce A. Ebersole Mary A. Cialone Mark D. Prater 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. RRA CE a Re lp TASK US Army Engineer Waterways Experiment Station Coastal Engineering Research Center PO Box 631, Vicksburg, Mississippi 39180-0631 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE DEPARTMENT OF THE ARMY March 1986 US Army Corps of Engineers 13. NUMBER OF PAGES Washington, DC 20314-1000 160 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report) Unclassified 1Sa. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of thie Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES Available from National Technical Information Service, 5285 Port Royal Road, Springfield, Virginia 22161. 19. KEY WORDS (Continue on reverse side if necessary and identify by block number) Computer model Diffraction Refraction Water waves 20. ABSTRACT (Continue am reverse side if necessary and identify by block number) The numerical model documented here, RCPWAVE, can be used to solve wave propagation problems over arbitrary bathymetry. The governing equations solved in the model are the "mild slope" equation for linear, monochromatic waves, and the equation specifying irrotationality of the wave phase function gradient. Finite difference approximations of these equations are solved to predict wave propagation outside the surf zone. Inside the breaker zone, an (Continued ) DD rons 1473 EDITION OF ? NOV 651S OBSOLETE Neer t JAM 73 Unclassified SECURITY CLASSIFICATION OF THIS PASE (When Data Entered) Une] ified SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) 20. ABSTRACT (Continued). empirical method is used to predict wave transformation. This method is based on a hydraulic jump representation of the entire surf zone. The model is ver- ified using laboratory and field data. A user's manual section is provided to aid potential users. This docu- mentation contains two examples illustrating application of the model. These examples describe job control language files, job submission procedures, sam- ple input and output files, and execution costs. Unclassified SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREFACE The model development documented here was authorized as part of the Civil Works Research and Development Program of the Office, Chief of Engineers (OCE), US Army. The research work unit funding this work, Regional Coastal Processes Numerical Modeling System, is part of the Shore Protection and Res- toration Program. Messrs. John H. Lockhart and John G. Housley were the OCE Technical Monitors during preparation and publication of this report. The study was conducted under the direction of Dr. James R. Houston, Chief, Coastal Engineering Research Center (CERC) of the US Army Engineer Waterways Experiment Station (WES); Mr. Charles C. Calhoun, Jr., Assistant Chief, CERC; and Mr. H. Lee Butler, Chief, Research Division. The report was prepared by Mr. Bruce A. Ebersole, Research Hydraulic Engineer; Mrs. Mary A. Cialone, Hydraulic Engineer; and Mr. Mark D. Prater, Research Hydraulic Engineer. The prototype data used in the model verification procedure were supplied by members of the staff of CERC's Field Research Facility, particu- larly Messrs. William A. Birkemeier and H. Carl Miller. This report was edited by Ms. Shirley A. J. Hanshaw, Publications and Graphic Arts Division, WES. Director of WES during publication of this report was COL Allen F. Grun, USA. Technical Director was Dr. Robert W. Whalin. CONTENTS AWN SS s\goqoco odo clo Oo:d1al0 0.01010 6 ard 010.0 00. :010 d.010 010 010.010 001001051010 :01010:9.0:0.0.0. 9.0.0.0 010 PART I: JONES COPDOKE MIO 3.4 6.6.6 ais ool 6 doo Oo Cio CigidIMIO 010.9 O10 O1O\d1O-0'5:0/010 01010.0.9:6.0,0 PART II: REGIONAL COASTAL PROCESSES WAVE PROPAGATION MODEL (RCPWAVE) . Background) Mmformalte dome. /< roe) ion ellepenelole lolol lsitalee Elliptical Shoal Case: Comparison With Laboratory Data............. CERC's FRF Cases: Comparisons with Prototype Data.................. Verification of the Wave Breaking Scheme: Comparisons with LfAleYONeEVOl Ay WENGE oo ocoou DIDO 6D D000 0 G00D0 010d 0010100000 00:00.0.00000.00000.0 PART IV: MODEL EXECUTION ON THE CONTROL DATA CORPORATION COMBUAVING TSMSIDE MEE peer a relie revere cileieloloxohei(« cchei eles olesreile) ielie) olleleelleNeeyoileKe ice enol GeneraleCommentsSeyweenarencpekencneten ners cheiels cia encuoelioh= lois tedeyiol(sKellaiops\eiteleliol el oReNcle) mek kee CYBEREGOS J obNControlmleang agers sic cusses otis elalielals citer oisieko rs) lel vevenorenerens Submi Goanpasthey CYBER GO5sBAcchmJObDe ses. <)sre-i erento ays ste eyetelercnsict sae otetonet= CYBERMZ OS RJ obmControli ban guage sera a olene cleo) ene seyciiel.s: creli-Werel'e) )oells)i«) MemsiensioRelleke Submitting ther CyBPRe2OSm Bat ehe JOD. ao ccs) «ieieielelellolel/onel sislereislieis) «hel eieloreho slere Iijgje FILS obo be Hoos OS ONO UO OOOO UUD UO DOOOCOUUMU OAC DD UCDO OGD 0000000 OUE PU BEAMS Mer reryelciereickerenay enetsrove ieueltcie feilepeyieyiele]/sellelonelelieliehe\elehetteus)(eVel sIhelion erate hetelte PART V: MODDED WAR PIOMCAT TONS 2 cuca yeret «i.eiei 6).0\ ciel +10) o/(ej/e\(elielis\is\ o)ts) o\le\iaile\is 's\(o) ee\\enel/oNetelloRetien General Comment Shere cratcncrexsnerceetemoerceey slotelisholerelesolevicnelovehenelslKenekclever or eleKerolensnotener one Example I: FRF Pier, Duck, North Carolina...............2--ee+eeee- Exampille Il: Homer Spit, Alaska... 2.2 2c. cece cee sec ewes seeerne Corie CoMmprielsonsicgogacdecccnccoccocddondOUdu 00 dG OD Udb EHO eOoD00000000 PART VI: GRU INTERPOLATION (PROGRAMM GINIPRER) yrre tei erevel es c1sie ail elelerelotckel neers General eiCommente Sheva am reneiercieicronciererereiel clamor ebenelich st ebenobsherercheueleletenel olen RetehMet Mois Executing INTPRCP on the CDC Computing System...........222eeeeeeee- Trap Ue ana Oui pues ih) UMS Slee raes crreriosiostctierrei te otis lo teuollelie’/a\ielvolrofaile)islie\ie\ ovellolelis\ey +lisiteitoleiielie) -eneye Grid@interpollatiion Exampilichyic. siers «seine eilcie/ oi e)iel eel elleile) sielle! 1/2] «1 el eilail=) +) oile)ieJisliolenelle PART VII: CONCLUSIONS AND RECOMMENDATIONS. .........cccecccceccscesessenns REBERENCES ycwrrorerstetel ones telicnetenedororcvoicrousnens oust teneueveleneietoleVeie) siaslolaleyaleleel ol hele lolon tebe Moto RoteKe APPENDIX A: VERIFICATION OF MODEL RESULTS USING THE ELLIPTICAL SHOAL PAB ORATO RYE SES Tye D ANNAN ce sisrelio fol st eke stevetiol sie ieieliodeis\loreellelelolele) sKeletolel=meieltaKoloKs APPENDIX B: VERIFICATION OF MODEL RESULTS USING FIELD RESEARCH EAC EYER (ERED) WER OL ODP Ee DAA yearopetcteres sisvetenatnenenoieysiclsieveteneteltenentensusts APPENDIX C: VERIFICATION OF MODEL RESULTS USING BREAKING WAVE DATA COLEECTED? IN) LABORATORY EXPERIMENTS) oie erie ris cite, «lleilelteitevels «elses APPENDIX D: LINE-BY-LINE DESCRIPTION OF JOB CONTROL LANGUAGE FOR EXECUTING RCPWAVE, ON) THE: CYBER 865, COMPUTER: 3.02). 0). 1-110 cree APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX I APPENDIX J APPENDIX K LINE-BY-LINE DESCRIPTION OF JOB CONTROL LANGUAGE FOR EXECUMING RCRWAVEW ON) THE (CYBER] 205) (COMPUTER Gere). cvcceie 0) seco) ee REEWAV EME ROGRAMPIEMS TaN Gratien este eilellelerelieiisierctacs ol creel celererelerene tered eke tele SAMPLE FILES--FIELD RESEARCH FACILITY PIER, DUCK, NORTH CAROLINA, WAVE, PROPAGATION EXAMPLE sc) ceuers c «/e1le)'s 1s ole) «eee ©) 61,0) 01\01'0\/0\re SAMPLE FILES--HOMER SPIT, ALASKA, WAVE PROPAGATION REGIONAL COASTAL PROCESSES NUMERICAL MODELING SYSTEM RCPWAVE--A LINEAR WAVE PROPAGATION MODEL FOR ENGINEERING USE PART I: INTRODUCTION 1. The "Regional Coastal Processes Numerical Modeling System" research work unit is part of the US Army Corps of Engineers (Corps) Shore Protection and Restoration research program. Its goal is the development of a modeling system that can predict coastal processes on a regional scale so that coastal changes resulting from natural forces and man-made structures and modifica- tions can be determined on a regional basis. All important physical processes that determine coastal changes over a region will be considered in the sys- tem's development. Long-wave (e.g. tide and storm surge) hydrodynamics, short-wave (e.g. swell and wind sea) propagation, and associated currents and setup/setdown will be addressed. These wave phenomena will be used as forcing functions to drive models which calculate alongshore and on- offshore sediment transport. Sediment sources and sinks such as sediment discharge from rivers, dredging gains or losses, and dune erosion will be considered in the sediment models. The modeling system will provide a tool for predicting coastal ero- sion and deposition, paths of sediment movement, and ultimate fates of coastal sediments. 2. All component models comprising the system must be capable of per- forming regional scale simulations in a cost-effective manner. Regional scale implies an area of interest with horizontal length scales of up to tens of miles and simulation times ranging from days to years. These requirements im- pose severe restrictions on candidate models. Individual models must also be compatible so that they can interface with one another in an efficient manner. Some examples of compatibility are (a) solutions from different models com- puted at identical spatial locations and (b) input/output information common to different models retrieved/stored using identical formats. 3. A philosophy for development of the modeling system has been adopted which provides direction to the work unit research. The aim is to develop (and/or obtain) and link a series of models so that all important physical processes are simulated to a predetermined level of sophistication. This milestone will occur approximately 2 years before the scheduled conclusion of the work unit. Component models comprising the initial system are determined by: (a) available models within the Coastal Engineering Research Center (CERC) addressing the important physical processes, (b) other (outside CERC) state-of-the-art methods for modeling these processes on a regional scale, and (c) the need for having a field oriented product in the near future. The framework designed for linking these models into a usable system will allow for integration of more sophisticated models when they become available. Re- search addressing perceived weaknesses in the system models will be conducted concurrently with work done to bring the system to its initial level of sophistication. 4, Any technology created as an interim product, which can immediately aid Corps field engineers and can be easily transferred to them, will be made available. This report documents such a product. The Regional Coastal Pro- cesses Wave (RCPWAVE) Propagation Model can be used to predict linear, plane wave propagation over a "regional" area of arbitrary bathymetry. This model currently forms the initial level of sophistication for the short-wave model- ing component of the regional system. PART II: REGIONAL COASTAL PROCESSES WAVE PROPAGATION MODEL (RCPWAVE) Background Information 5. Linear wave theory was chosen as the initial level of sophistication for the short-wave modeling component because, historically, it has been shown to yield fairly accurate first order solutions to wave propagation problems. Considering both accuracy and cost, it is currently the most feasible way to model waves on a regional scale. Modeling short-wave processes using either a fully two-dimensional nonlinear wave theory or a two-dimensional spectral re- presentation of irregular waves is presently impractical for the types of ap- plications anticipated for this modeling system. 6. Much of the early work addressing the problem of linear, monochro- matic wave propagation was based on wave ray methods and the manual construc- tion of refraction diagrams (see Johnson, O'Brien, and Issacs (1948); Dunham (1951); and Pierson, Neumann, and James (1952) for examples). During the 1960's and early 1970's the refraction problem was solved in a more efficient way through the use of the computer (for examples see Harrison and Wilson (1964), Dobson (1967), Noda et al. (1974), and Rabe (1975). Refraction theory fails in regions of complex bathymetry where waves are strongly convergent or divergent. Crossing wave rays results in the computation of erroneously large wave height estimates. Strongly divergent wave fields manifest themselves in regions of unusually small wave heights. Laboratory and prototype observa- tions show that refraction theory is inadequate under these conditions (Whalin 1971 and 1972). 7. Inclusion of diffractive effects into the equations governing wave propagation allows wave energy to be diffused from regions of convergence to regions of divergence. Berkhoff (1972 and 1976) derived an elliptic equation approximating the complete wave transformation process for linear waves over an arbitrary bathymetry constrained only to have mild bottom slopes (hence the designation "mild slope equation" (Smith and Sprinks 1975)). The mild slope equation can be expressed in the form Cc lke: ao Os cI) rE a (cc, aX , + ay ce, ay DRO o = 0 Gib) x and y = two orthogonal horizontal coordinate directions c(x,y) = the wave celerity (= o/k) o = angular wave frequency (defined to be 2n/T) k(x,y) = wave number given by the dispersion relation, on = gk tanh (kh) T = wave period ee) = group velocity (= 40/ak) o(x,y) = complex velocity potential g = acceleration due to gravity h(x,y) = still-water depth 8. Numerical solution of this equation for the velocity potential field is an effective means for solving the complete wave propagation problem. The equation can be solved using either finite element (Berkhoff 1972 and Houston 1981) or finite difference methods (William, Darbyshire, and Holmes 1980). Since transmission and reflection boundary conditions are easily implemented into these solution schemes, this approach is a popular one for modeling tsu- nami propagation and for solving problems involving the response of harbors to short and long waves. This method becomes computationally infeasible for large scale, open coast, short-wave problems because of its great expense. Numerical solutions of Equation 1 are only practical, as a rough rule of thumb, when the dimensions of the spatial area of interest are no more than 10 times the length scale of the wave lengths being considered (Berkhoff, Booy, and Radder 1982). 9. An alternative method based upon a simplification of this equation has recently been developed. This method alleviates the computational bur- den imposed by a direct solution of Equation 1. The velocity potential can be separated into a forward scattered and a reflected component. By neglect- ing the reflected part and assuming that diffractive effects in the direc- tion of propagation are much less than those perpendicular to the direction of wave advance, the following equation for the forward scattered wave can be derived: @ -O- = x | * lel LAT: ine) ay ie) ie) a edi ao P ax (kee) ‘dae oe ay (ce, =) (2) where i = V-1 and x is now defined as the principal direction of propa- gation. Here, the velocity potential describes only the forward scattered wave field. The assumption made above, concerning the relative magnitude of the diffractive effects, changes the character of the governing equation from elliptic to parabolic. Very efficient computational techniques exist for solving this type of equation. Candel (1979), Radder (1979), Lozano and Liu (1980), Tsay and Liu (1982), Berkhoff, Booy, and Radder (1982), Booij (1981), and Kirby (1983) all applied this approach to study the problem of wave propa- gation over complex bathymetries using finite difference solution techniques. 10. The "parabolic approximation" method, as it is called, has the fol- lowing disadvantage. It requires that one grid coordinate be approximately parallel to the predominant wave direction. This requirement can conceivably result in erroneous solutions to problems involving complex bathymetries where a dominant wave direction may not be clearly defined. Booij (1981) examined errors associated with the application of different parabolic approximations to solve the problem of oblique wave incidence over a horizontal bottom. To date, nothing has been documented concerning errors which may result from using this method to model wave incidence over arbitrary bathymetry. This di- rectional restriction also implies that more than one grid system may be re- quired in order to simulate a wide range of incident wave directions. The parabolic approximation method is a powerful tool for predicting linear wave transformations, but, it does have some deficiencies. These unaddressed prob- lems currently preclude its incorporation into the regional modeling system, as it is envisioned. 11. The model presented in this report, RCPWAVE, is an alternative ap- proach for solving the open coast wave propagation problem. It addresses both processes, refraction and diffraction, and can be applied on a regional basis quite economically. The model also contains an algorithm which estimates wave conditions inside the surf zone. This wave breaking model is an extension of the work of Dally, Dean, and Dalrymple (1984) to two horizontal dimensions. Kirby (1983) implemented their one-dimensional breaking model into his para- bolic approximation model. Any short-wave propagation model integrated into the regional system must address the problem of wave transformation within the surf zone where many of the physical processes interact and move sediment. Wave Transformation Outside the Surf Zone Theoretical Basis 12. The velocity potential function for linear, monochromatic, plane waves can be represented by the expression o = ae (3) where a(x,y) = wave amplitude function equal to gH(x,y)/2o0 H(x,y) = wave height s(x,y) = wave phase function Here again, the velocity potential function only describes the forward scat- tered wave field. No considerations are given to wave reflections. By sub- stituting this expression for the velocity potential into Equation 1 and solv- ing the real and imaginary parts separately, two equations can be derived (Berkhoff 1976), namely, 2 2 : a + a + al Va-V(cec_)]}+ 1 - \vs|° =0 (4) ppeall Tey g 8 v-(a-ee, Vs) = 0 (5) where the symbol Vv denotes the denotes the horizontal gradient operation. 13. Together, these equations describe the combined refraction and dif- fraction process. Diffraction is often erroneously described as the propaga- tion of energy along wave crests which are defined to be perpendicular to the wave phase function gradient Vs . Equation 5 shows energy is still propa- gated in a direction perpendicular to the wave crest. Diffractiwe effects do change the phase function as a result of significant wave height gradients and curvatures. These changes cause the local wave direction to vary. If dif- fractive effects are neglected, Equations 4 and 5 reduce to those describing pure refraction in which the wave number represents the magnitude of the phase function gradient. 14. Linear wave theory assumes irrotationality of the wave phase func- tion gradient. This property can be expressed mathematically as vx(Vs) = 0 (6) The phase function gradient can be written in vector notation as > 5 Vsil=" |Vs|cosmeham-em||Vs|msinwely (7) > > Where i and j are unit vectors in the x- and y-directions, respectively, and (x,y) is the local wave direction. Equations 6 and 7 can be combined to yield the following expression: Ee ( |vs| sin G), - = ( |vs| cos 0) = © (8) If the magnitude of the wave phase gradient is known, local wave angles can be calculated from Equation 8. Similarly, Equation 7 can be substituted into Equation 5 to yield es (s%c, |vs| cos 9 + a (ace, |vs| sin ) = 0 (9) This form of the energy equation can be solved for the wave amplitude function a once the wave phase characteristics Vs and 6 are known. The wave height can be determined and is proportional to the amplitude function, since wave frequency is constant. 15. Equations 4, 8, and 9, along with the dispersion relation, describe the combined refraction and diffraction process for linear plane waves subject to the restrictions that the bottom slopes are small, wave reflections are negligible, and any energy losses are very small and can be neglected. The numerical solution scheme used to solve these equations is presented in the next section. These equations are assumed to be valid outside the surf zone. The method used to determine wave characteristics inside the surf zone is de- scribed later. Numerical solution 16. The three governing equations (Equations 4, 8, and 9) are solved using numerical methods. Partial derivatives within the equations are approx- imated using finite difference operators. Finite difference solution methods require the construction of a computational grid system or mesh. Solution ac- curacy is directly related to resolution within the grid system. Discussion 10 throughout the text will refer only to grid systems comprised of constant sized, rectangular cells. RCPWAVE is capable of computing solutions on vari- ably sized, rectilinear grid systems. Technology for creating variably sized grids, which are compatible with the wave model, exists at CERC. 17. Figure 1 shows nine rectangular cells which make up a small part of a larger mesh. Each cell has a length equal to Ax in the x-direction and Ay in the y-direction. The maximum values of i and j are M andy Ni % respectively. y - AXIS j=1TON i=1TOM x - AXIS Figure 1. Definition of coordinate system and grid cell conventions used in the model 18. All variables which vary as a function of space are defined at the cell centers. For any dependent variable F , the following finite difference operators are used to approximate certain partial derivatives of F at the position (i,j): ala af Ss i i+1 ; i+2 i+3 (10) ax (Ax) a) Panag 2 als Pa sel aot D (11) ay (Ay) de) Pa es Bias (42) ae 2Ax BE (Gielen (ea ay 2Ay Equations 11 and 13 are central differences, and Equations 10 and 12 are back- ward differences. All four expressions have the same order of accuracy. 19. The magnitude of the wave phase function gradient at any point (i,j) is computed from the following expression, Zay. - da. + 4a, - a. | vs| Ke ¢ i. | bd) i+1,j i+2, j a eh ad Oke (ee E ell ended _ 1 fi 2 x“ ce A 5 (Ay) Big (14) ‘=3cc + 4ee -cc : 3a; 5 + MAi.y 5 7 Fase Bij Bist, j 8142, 5 2Ax 2Ax cc = ce Airy edi sae ed Bi jel SUT 2Ay Ay | This equation was derived by approximating the partial derivatives in Equa- tion 4 using the finite difference operators given in Equations 10 through 13. The reason for selecting backward finite differences to approximate the x-derivatives, specifically the curvature, will be discussed later in this section. 20. Equations 8 and 9 can both be expressed in the following general form: 2 ey LEG) (15) If partial derivatives in both the x- and y-directions are estimated using central differences about the point i-1/2,j , then an approximate form of Equation 15 can be written as Bi zi v9 [Aska itch) Het 0 i, j+1 Ltt) 20H AIG) The partial derivative aG/dsy at position i-1/2,j has been represented as a weighted average of its values at locations i,j and i-1,j . The value of the weighting factor W used in RCPWAVE is 1.0. This choice implies that an implicit solution of the equation is required. One additional approximation is made by using the following weighted sum: Pat ane +(1- 2a)F. + aF. (17) J iy j=! to represent the variable F at position i,j . Here a is another weight- ing parameter. The value of a is set to 0.167 in RCPWAVE. This "dissipa- tive interface" (Abbott 1975) is used to enhance the stability of the numeri- cal scheme. Substitution of Equation 17 into Equation 16 results in the following expression: F =F! feta See +0 G1) = BOE + aF ja4 G. - G. } Came -G. . i-1, j+1 i-1,j-1 Agate i,j-1 + AX ( Phy +(1- wl (18) The finite difference formulation of Equations 8 and 9, which will be de- scribed next, is identical to that used by Perlin and Dean (1983). Their choices for W and a were 1.0 and 0.25, respectively. 21. The finite difference form of Equation 8 is derived by substituting the following expressions for F and G _ into Equation 18: F = |vVs| sine (19) G = -|Vs| cos @ (20) These substitutions result in the following equation in which the sine of the local wave angle at the location i-1,j is the quantity to be determined, thus ; Medien i" sin 6,11 5 = RS ae [elves jar sin @; 341 * (1 2a)|vs| 5 sin @; | + alvs|s 54 sin eal) - HEX (les | a set COS 85 4 444 (21) SS) a cos oe) - ae (lela ge cos Oriani -1¥S] 5 jot cos °1,3-1)] 22. Similarly, using the substitutions F = acA (22) G = a°B (23) where A = ec, |¥s | cos 0 (24) B= ec, |¥s| sin 0 (25) the finite difference form of Equation 9 becomes 14 2 2 2 a) eens (ef, serfs, er til puced ages Aaiaat oa} j-18i,5-1) WAX (22 (26) + B - ae B 2Ay i-1,j+1 i-1, j+1 i-1,j-1 i-1,j-1 (1-W)Ax/ 2 2 ~ ay Suse a acapsay hy! This equation can be solved for the wave amplitude function, and subsequently the wave height, at the location i-1,j . The remainder of this section de- scribes the procedure used to solve the set of approximate Equations 14, 21, and 26. 23. Model input (described in detail in Part IV) includes values of the deepwater height H direction 95 , and period T of waves to be simu- ’ lated. It also ets specification of the bottom bathymetry throughout the grid. The wave number, which is related to the wave period and the local water depth through the dispersion relation, is computed at every cell. Wave number is used as an initial guess for the magnitude of the wave phase func- tion gradient. The wave celerity c and the group velocity Cy are func- tions of the wave period and wave number. Therefore these variables can be calculated at each cell. 24. From Snell's law, Sime) | nee 8 (27) Chae meee fo) where c, is the deepwater wave celerity (defined to be gT/2n ), an estimate of the local wave angle is calculated everywhere. This estimate assumes that the bottom contours are parallel with the y-axis. If the bottom bathymetric contours make a known nonzero angle with the y-axis, a better first guess for the wave angles can be computed. The new approximation is sin (9 -@_) Q;o 1D where oF defines the contour angle. The local wave angle, deepwater wave angle, and contour angle follow the angle convention shown in Figure 2. The contour angle is an input parameter into RCPWAVE. y-AXIS POSITIVE 6, NEGATIVE 6, 0 necarive| 96 POSITIVE ] Aa t) x - AXIS 0. =DEEPWATER WAVE ANGLE fe) @ =LOCAL WAVE ANGLE 6, =OFFSHORE CONTOUR ANGLE Figure 2. Definition of angle conventions used in the model 25. Wave heights at each cell are estimated as the product of the deep- water wave height, a shoaling coefficient rsd and a refraction coefficient Kee Chus r Hig= HokrXs (29) where cos 9, Vie “r = \eos 6 (30) and 1 1/2 (31) + sinhii(ekh) tanh (kh) sour (: 2kh The dispersion relation, Snell's law, and this simple estimator of the wave height allow an initial guess to be made for the variables of interest throughout the grid system. 26. The solution scheme implements the following marching procedure once initial guesses for the variables of interest have been made. Starting at the offshore row designated by i=M-3 , Equations 21 and 26 are used to compute wave angles and then heights along the entire row (from j=2 to j=N-1). Wave height is used interchangeably with amplitude function since one is directly proportional to the other. 27. Wave angle and height solutions along a given row are solved iteratively because of the implicit differencing formulation used. Calcula- tions of the wave angle (actually the sine of the wave angle) and the wave am- plitude function are reiterated until the average change (along a row) in each variable from one iteration to the next is less than some tolerance. These convergence criteria, 0.0005 for wave sines and 0.001 ft* (or a metric equiva- lent) for wave heights, are suggested values for prototype applications. They can be easily changed by modifying the source code using the method outlined in Part IV. 28. This solution considers only refraction since the wave number k is used as an estimate of the magnitude of the phase function gradient. Equa- tion 14 is then used to compute the true magnitude of the wave phase gradient. This new wave number accounts for the effects of diffraction. Backwards dif- ferences are used to approximate the x-derivatives because they require only information which has already been computed. Next, Equations 21 and 26 are again solved in order to compute the wave angles and heights using these new wave numbers. This procedure is repeated along the row under consideration until the change in new wave number, from one iteration to the next, is less than 0.5 percent of the newly computed value. This condition must be met at each cell along the row. As a row of new wave numbers is computed, the values are filtered in the y-direction using the method of Sheng, Segur, and Lewellen EEE * To convert feet to metres use a conversion factor of 0.3048. aly (1978). This filter removes cell-to-cell oscillations introduced as a result of the differencing scheme used to compute the new wave numbers. Row-by-row marching proceeds until solutions are computed along row i=2. 29. Lateral boundary conditions for a row are specified at the conclu- sion of calculations for that row. The value of all variables at cells j=N and j=1 are set equal to their values at cells j=N-1 and j=2 , respec- tively. This boundary condition implies that the change in the variable in the y-direction is zero. The condition is most valid when the bathymetric contours are nearly straight and parallel to the y-axis. For this reason it is recommended that users orient their grid system so that the y-axis is nearly parallel to bottom contours along the lateral boundaries. 30. Boundary conditions along the seaward extent of the grid are used to initiate the shoreward marching algorithm. They are computed from deep- water wave input supplied by the user along with the following assumption. Bottom contours extending from the offshore grid row i=M out to deep water are assumed to be straight and parallel to a line making an angle of 8, with the y-axis. In other words, Snell's law is assumed to be valid from deep water to the outer boundary of the grid system. No inshore boundary condi- tions (along row i=1) are required because of the foreward marching solution scheme. Wave Transformation Inside the Surf Zone Theoretical basis 31. Waves approaching the very nearshore zone tend to steepen and even- tually break because of decreasing water depths. Shoreward of this breaking point dissipative energy losses due to turbulence strongly influence the wave height. Linear theory does not allow for prediction of the breaker location nor for wave transformation across the surf zone. Instead, empirical and ap- proximate methods must be used to describe the breaking process. 32. The first aspect to consider in surf zone transformation of waves is incipient wave breaking. Iwata and Sawaragi (1982) reviewed many criteria for determining wave characteristics at the breaking point. One which is ap- pealing because of its basis on wave physics defines breaking as the point when the particle velocity at the wave crest exceeds the wave celerity. The following formulas: 18 and b L enh, H. = 0. 142-0 ‘tanh ( (33) b b H, = breaking wave height = water depth at breaking Ly = wave length at breaking by McCowan (1891) and Miche (1944), respectively, are based on this criterion. Equations 32 and 33 were derived for solitary and periodic shallow-water waves, respectively, in water of uniform depth (Iwata and Sawaragi 1982). A breaking height predictor based on wave energy flux was developed by Komar and Gaughan (1972) and is given by H. = (gy (mre) (34) where «* is a dimensional coefficient equal to 0.39. Field and laboratory data have shown this predictor to be quite accurate. Other incipient breaking criteria have been developed by fitting empirical relationships to breaking wave data. These methods are not derived from any theoretical considerations of wave physics, yet results derived using them agree very well with observed data. The most widely used of these criteria are those developed in Equa- tions 35, 36, and 37 by Le Mehaute and Koh (1967), Goda (1970), and Weggel (1972), respectively. These criteria are as follows: H -1/4 % s10) WA H, = 0.76 HL| 7 m (35) fo) where Lo = deepwater wave length m = bottom slope hy, 4/3 H, = 0.17L5)1 - exp) -1.5 --(1 + 15(m)) (36) fe) Ly and 19 H, = ——2.— (37) where o(-19m)] (-19.5m)] 43.7511 1.56/11 +e a b 33. All of these empirical methods give reasonable approximations of the incipient breaking wave height. In choosing a criterion for inclusion into RCPWAVE, the following factors were considered. The criterion should ac- count for bottom slope and wave period since field and laboratory tests show these parameters to be important (Iwata and Sawaragi 1982). It should not depend on deepwater parameters alone because the transformation algorithm must be capable of modeling multiple breaking and reformation. The Weggel (1972) and Goda (1970) criteria satisfy both requirements. The former was selected for inclusion into RCPWAVE. 34. Once the incipient breaking point is defined, a mechanism is needed to transform the breaking wave across the surf zone. Historically the wave height has been assumed to be proportional to the local water depth throughout the surf zone. The constant of proportionality was assumed to be about 0.8. Field and laboratory data have shown that this approximation consistently overestimates actual wave heights within the surf zone (Dally 1980 and Thorn- ton and Guza 1982). Other formulations have been developed and applied suc- cessfully by researchers to calculate surf zone wave heights. Most are of the following form: 9(Ec_) ae a sas (38) ax = where Ec, is the energy flux associated with the breaking wave and 6 isa term representing the rate of energy lost due to bottom friction, turbulence, and other dissipative processes. 35. Divoky, Le Mehaute, and Lin (1970) considered the dissipation in a breaking wave to resemble that in a hydraulic jump. They assumed that the change in energy flux could be approximated by 20 a(Ec_) (y, =Y4 \3 = 89 | hy ¥ (39) where p = water density Q = flow across the jump Y, = water depth on the high end of the jump Y5 = water depth on the low end of the jump For water of uniform depth, they assumed that Y5 =whi+! Ale vand Yy = h + BH where 8 is a coefficient related to the percentage of the wave height covered by foam. Battjes and Janssen (1978) also used a hydraulic jump repre- sentation of wave breaking. They used the following expression: 9(Ec_) ye ax =a* 0210 To (40) where a* is a coefficient of order one. Mizuguchi (1980) modeled surf zone energy loss as, a(Ec_) 2 g kH ax = GRE (4) ) where Vis is a coefficient of turbulent eddy viscosity. Results derived from this model compared quite well with experimental data, but any physical rea- soning behind the use of the eddy viscosity formulation is, as Mizuguchi (1980) states, obscure. Horikawa and Kuo (1966) developed an analytical scheme using second order solitary wave theory and theoretical expressions for dissipation due to bottom friction and turbulence. Their governing equation contained two coefficients, one for each dissipative mechanism. 36. The transformation algorithm selected for use in RCPWAVE (Dally, Dean, and Dalrymple 1984) uses the same energy flux basis as the models men- tioned above. However, instead of using a hydraulic jump to represent energy loss in a single breaking wave, the form of the hydraulic jump energy loss is used to approximate losses across the entire surf zone. Through analogy with energy flux in a channel, the following equation is postulated: a(Ec_) pl oh ape, Es lec, ; (F,),| (42) fall where k = rate of energy dissipation coefficient (set equal to 0.2 in RCPWAVE) (cg) = stable level of energy flux that the transformation S process seeks to attain The right-hand side of Equation 42 is simply a dissipation term. The sub- script s is used to denote the stable level of some quantity. Substituting the linear wave theory estimate for E (E = 0.125 ae) into Equation 42 re- sults in the following expression: 9(H@c_) ee ee =i! Cg i (43) 37. Various field (Thornton and Guza 1982) and laboratory (Horikawa and Kuo 1966) experiments have shown that, well into the surf zone, the wave height tends toward a stable value which is proportional to the local water depth. This relationship can be expressed as where = ! = stable wave height Y = proportionality coefficient (set equal to 0.4 in RCPWAVE) Equation 43 can now be rewritten as 2 a(H © ) ax h g - 38. This surf zone wave transformation model can be incorporated into the conservation of wave energy equation (Equation 5) by simply adding the dissipation term D to the right-hand side. The function D must now repre- sent dissipation in the direction of wave propagation. Also for dimensional consistency, the term D must be multiplied by the wave celerity and the mag- nitude of the wave phase gradient, and the wave height must be replaced by the wave amplitude function. In vector notation, the energy equation becomes v-(2°c0,95) = = | sPespiv9 - (Ga) haces \vs| é (46) 22 This equation can be thought of as being valid both inside and outside the surf zone. Outside, the coefficient « is zero, and the equation reduces to Equation 5. 39. Discussion relating to wave transformation within the surf zone has addressed the problem of determining wave heights. The problem of wave phase must be addressed also. Diffraction effects are assumed to be negligible inside the surf zone. Therefore, the wave number k is assumed to accurately represent the magnitude of the wave phase function gradient. The linear wave theory assumption that the waves are irrotational also will be assumed to re- main valid inside the surf zone. Consequently, wave angles inside the surf zone are computed in the same manner that was used outside the surf zone. Numerical solution 40. The numerical procedure for computing wave angles inside and out- side the surf zone is the same. This section documents only the solution scheme used to determine breaking wave heights. The finite difference form of the wave energy equation outside the surf zone (Equation 26) can be expressed in the following form: ac ty F + Ax G (47) i-1,j PA odes where — 2 2 F = Casale a eis Bae + oo eed 2 2 tb fie leu lentes Si 2Ay 2 2 iors See edie je = Set Ea ene 2Ay Bee Coa (Ws esirie 8 Avec |vs| cos 8 8 With the inclusion of the dissipative term, Equation 47 becomes 23 a. a = ea a ee (48) where D* represents the finite difference form of the dissipation term on the right-hand side of Equation 46. Reiterating, the dissipation term is an average value along the wave path. The wave path is determined by the local wave angle at the position i-1,j which has already been computed. There- fore, the average along the path is an average of information at cell i-1,j and another cell whose position is denoted by ikey,jkey . The procedure used for determining the location of this cell will be presented later. 41. The term D can be written in finite difference form as |vs| + (ace | Vs | (a°co, key, key ( g hens (49) Qe One. (s:) y hee IVS| se hon 2 Ya Ce lvs|5_, , Wa, where With some algebra, Equation 48 can be reorganized so that the amplitude func- tion at the position i-1,j only appears on the left-hand side of the equa- tion. Therefore, the energy equation inside the surf zone can be numerically solved using the same procedure which was used to solve it outside the surf zone. 42, The location of the cell denoted ikey,jkey is found using the following procedure. "Areas of influence" are determined by extending lines from the center of the cell i-1,j to the midpoints between the surrounding cell centers (Figure 3). Angles are computed from the x-axis to these radial lines. The local wave angle calculated at cell i-1,j is compared to each of these angles in order to determine the nearest, prior cell along the wave path. For example (refer to Figure 3), if the local wave angle is greater than 6 but less than 6 2 ikey = i and jkey = j+1. 1? then cell i,j+1 is the cell of influence and 43, A flow chart describing the wave height computation is shown in 24 CELL CENTERS Figure 3. Schematic drawing showing cell of influence conventions used in the wave breaking scheme Figure 4. The wave amplitude function is computed from the energy equation assuming no dissipation. The amplitude function is converted to wave height and compared to the stable wave height yh . If the wave is less than or equal to this stable level, the wave is either inside the surf zone, having been transformed to a state below the stable level, or it is outside the surf zone. In either case, no further transformation is needed. If the wave height is greater than yh , then additional wave transformation may occur. The cell of influence is located and tested to determine whether or not the wave has experienced prior breaking. If the wave is undergoing transformation in the cell of influence, it continues to be transformed. If the wave in the cell of influence is not being transformed, the local wave height is checked against the incipient breaking height criterion. If the height exceeds the allowable value, wave dissipation begins. The accuracy of the surf zone wave transfor- mation model has been verified using laboratory data of Horikawa and Kuo (1966) and Izumiya (1984). Comparisons between model results and these data are described in Part III. 25 Compute Wave Amplitude Function a Convert Wave Function to Wave Height H Test if Hs yh No Y Find Cell of Influence (ikey, jkey) Yes Was Wave Being Transformed in Cell of Influence No Yes Compute Breaking Depth h, from Weggel's Empirical Relationship Test if hy 2 h—— No Yes Recompute Wave Amplitude Function from Energy Equation with Dissipation Terms Included Continue to Next Computational Cell and Repeat Figure 4. Flow chart of the wave breaking scheme 26 PART III: MODEL VERIFICATION General Comments 44, Comparisons between model results and observed data were used to verify the model. Both laboratory and field data were used in these tests. The ability of RCPWAVE to simulate wave transformation outside the surf zone was checked using data collected during a laboratory experiment conducted by Berkhoff, Booy, and Radder (1982) and using prototype data obtained during a field experiment at the CERC Field Research Facility (FRF) in Duck, North Carolina. The next two sections describe these comparisons in detail. Fig- ures pertaining to the laboratory and field verification are located in Appen- dixes A and B, respectively. Only laboratory data were used to verify the surf zone wave transformation part of the model. These data were collected during one-dimensional flume tests performed by Horikawa and Kuo (1966) and Izumiya (1984). Both experiments considered only breaking of monochromatic, plane waves. The former experiment investigated wave transformation on a plane beach only; the latter involved tests using plane, stepped, and barred beaches. These comparisons are discussed in the last section. Figures per- taining to the wave breaking verification are located in Appendix C. Elliptical Shoal Case: Comparison with Laboratory Data 45, Berkhoff, Booy, and Radder (1982) performed a wave tank experiment in which wave conditions resulting from the propagation of a monochromatic, plane wave train over complex bathymetry were measured. The bathymetry con- sisted of an elliptical shoal superimposed on a plane beach. This geometry is shown in Figure A1. The shoal acts as a lens and focuses incoming wave energy into a strong convergence zone. This experiment provided a set of data which could be used to verify the ability of RCPWAVE to compute accurate solutions to problems where refraction theory breaks down. Wave height data were col- lected at many locations within this zone along the eight cross sections shown in Figure Al. RCPWAVE was used to simulate the same experiment. Simulated wave heights were then compared with observed data. 46. A finite difference grid mesh, which measured 25 m in the x-direction and 20 m in the y-direction was constructed. Rectangular grid eth cells measuring 0.25 and 0.20 m in the x- and y-directions, respectively, were used for the simulation. The center of the shoal was located at the point with x- and y-coordinates of 15 and 10 m, respectively. The equation de- scribing the outer extent of the shoal is given by y" 2 oA 2 Saline) ao (50) where x' and y' denote a local coordinate system whose origin is located at the center of the shoal. Also this coordinate system is rotated 20 deg in the clockwise direction relative to the x- and y-coordinate system. All length scales for both coordinate systems are measured in metres. Water depths, de- noted by h and measured in metres, were calculated from the following three equations, hig=s 0-4 Sya ora yy ii5)04 (51) h = 0.45 - 0.02 (5.84 - y')(outside the shoal boundary) (52) 2 2 1/2 he =0.45) = 0.0205. 845 — y's) 45053) =—9 025i = ‘2 - (e (53) (inside the shoal boundary) An incident wave with a period of 1.00 sec, a height of 1.06 cm, and a direc- tion of approach parallel to the x-axis was used as the deepwater boundary condition for the simulation. 47. Figures A2 through A4 show comparisons between the experimental data (open circles) and model results (solid line) for all eight profiles. Results are presented as profiles of relative wave height (observed wave height divided by incident wave height). A refraction analysis (presented in Berkhoff, Booy, and Radder (1982)) shows that a caustic occurs at a point be- tween profiles 2 and 3. Results show that the model is quite capable of accu- rately simulating diffractive effects at, and beyond, the caustic location. Consequently, it is a much more powerful tool for simulating wave transforma- tion than refraction theory alone. Berkhoff, Booy, and Radder (1982) and Kirby (1983) also numerically simulated this experiment in order to test their parabolic approximation models. Accuracy of their model results, using linear wave theory, is comparable to that obtained using RCPWAVE. Results obtained by Kirby (1983) are shown also in the figures (as a dashed line). Kirby showed that much of the discrepancy between simulated and observed data could be eliminated if a nonlinear wave theory were incorporated into the model. He incorporated Stokes' second order theory (which he showed was valid for this experiment) into his model, and the results also showed that nonlinear effects became increasingly important after the waves pass profile 3. 48. An interesting aspect of the RCPWAVE results is evident in pro- files 3, 4, and 5. The lobed features in the wave height variation are smoothed by the model. The cause of this smoothing is not known. It may be caused by the dissipative interface or the point-to-point filter used in the numerical scheme. The side lobes seem to be related to the occurrence of an amphidromic point where the wave phase becomes multivalued and the wave height variation contains a discontinuity. The solution scheme forces the magnitude of the phase function gradient to be single valued. This may also cause the local smoothing. The model is intended for use in open coast, prototype ap- plications. For these types of problems, this smoothing property of the model can certainly be tolerated. CERC's FRF Cases: Comparisons with Prototype Data 49. In addition to the laboratory verification, RCPWAVE also was veri- fied using field data collected at CERC's FRF in Duck, North Carolina. Bot- tom bathymetric contours in the area are generally straight and parallel to the coastline except in the immediate vicinity of the research pier. The pier's presence has caused the formation of a deep scour hole along much of its length. The complicated bathymetry, which has resulted from this hole, was one reason for selecting the FRF for field verification. Hubertz (1981) showed that a ray model using refraction theory alone proved incapable of sim- ulating observed conditions. Hubertz (1982) also showed that a short wave model which includes diffractive effects in its governing equations (the Sys- tem 21 Mark 8 proprietary model developed by the Danish Hydraulic Institute) could accurately simulate wave propagation in the vicinity of the pier up to the breaking point. 50. Another reason for selecting the FRF was the availability of wave data, both offshore and along the pier. During October 1982, an exten- Sive, 1-month field data collection program was undertaken. Two storms 2g occurred during the month, one lasting from 10-13 October and the other from 23-26 October. The latter was the more severe event. Prototype data col- lected during this month included bathymetric surveys conducted on October 16 and 27, continuous and synchronous wave data from six Baylor gages along the pier and an offshore Waverider buoy, radar imagery of the sea surface, and continuous tide elevation data. All wave data were available in a spectral form (energy density as a function of frequency). Estimates of significant height and peak period were provided also. Wave directions could be deter- mined from the radar imagery. The availability of clear radar pictures was ultimately the discriminating factor in selecting which time periods were con- sidered for verification purposes. 51. Six cases, or time periods, were ultimately chosen using the fol- lowing process. As stated above, only those times were considered when clear radar imagery was available. The number of candidate times were further re- duced by requiring that wave data be available within approximately 1 hr of the time the image was taken. Next, the wave spectum from the offshore gage was checked for spectral shape. Only times with single-peaked, fairly narrow banded spectra were considered. Six cases which met all the criteria are shown in Table 1. Table 1 Summary of Field Data Used to Verify RCPWAVE Time of Test 9 Radar Bathymetry Case Time Hy AB fe) Tide Imagery Survey Number Date G.m.t.* m sec deg m G.m.t. Date 1 10-13-82 1300 1.95 13.21 -23 0.12 1115 10-16-82 2 10-13-82 1400 We8i7, 14.22 -25 -0.18 VAS 10-16-82 3 10-15-82 1210 0.78 12.34 -25 0.78 1130 10-16-82 4 10-17-82 1200 1.56 6.87 43 0.91 1120 10-16-82 5 10-25-82 1900 3.10 12.34 -25 0.68 1950 10-27-82 6 10-25-82 2000 2.95 12.34 -25 0.63 1950 10-27-82 * G.m.t. denotes Greenwich mean time. 52. For each case the date and time of the recorded wave data are shown. The parameters Hy vel and oF are the deepwater wave characteris- tics used as input into RCPWAVE. The value of T was chosen to be the best 30 estimate of the peak spectral period and was made using data from the Wave- rider buoy and the seaward-most Baylor gage located at the end of the pier. The deepwater wave angle was computed using this peak period and a wave direc- tion estimated from the radar imagery. The time at which the radar image was taken also is given. Inherent in the procedure used to calculate the wave parameters in deep water is the assumption that the bottom contours seaward of the pier are straight and parallel. This assumption is quite reasonable for this stretch of coastline. The deepwater wave height represents a significant height and was computed using the peak period, deepwater angle, and the sig- nificant height recorded by the offshore Waverider buoy. The recorded wave spectra at the offshore gage are shown for all six cases in Figure B1. 53. Bottom bathymetry is required as model input. The total water depth matrix, used in the model, is computed by simply adding some tidal ele- vation to each depth value. Depth values were taken from one of two surveys shown in Figure B2. The particular survey used for each verification case is shown in Table 1. The tidal elevation (relative to mean sea level (MSL)) also is given in Table 1. The areal extent of each survey is identical, covering 1,200 m in the y-direction and 900 m in the x-direction. The orientation of the survey axes was adopted for use in constructing the model grid system. The x-axis is parallel to the FRF pier. Actual depth values (relative to MSL) were provided for each cell of a grid comprised of 75 cells in the x-direction and 50 cells in the y-direction. This grid completely encompasses the sur- veyed region. Cell dimensions are 12 and 24 m in the x- and y-directions, respectively. 54. Comparisons between simulated and observed significant wave heights along the pier are shown for each case in Figures B3 and BY. For these tests, the model is being used to propagate some amount of energy (here, designated by the significant height) with a single frequency and some mean direction. By requiring that the radar imagery be clear and contain only a unidirectional wave train, only waves which are nearly planar (long-crested) are being con- sidered. Since most of the wave spectra are narrow-banded (with the exception of Case 4), the cases being considered represent nearly monochromatic condi- tions. Therefore, assumptions inherent in the model's governing equations are essentially upheld, and the model should be able to simulate these conditions. Results show that RCPWAVE accurately predicts wave propagation for these types of wave conditions over a complex bottom. In all cases the scour hole causes 31 wave energy to be propagated away from the hole causing a reduction in wave height along the pier. Results from Hubertz (1982) substantiate this observa- tion. The trend of the wave height variation along the pier for Case 4 also is accurately simulated. The magnitude of the simulated significant height consistently underestimates observed data by about 0.1 m. The closeness of fit for this case, which involves a wider spectral bandwidth, suggests that the model may provide a useful method for predicting spectral wave transforma- tions if the waves have a small directional spread. More research is needed to test this hypothesis. Verification of the Wave Breaking Scheme: Comparisons with Laboratory Data 55. A number of numerical simulations were performed in order to verify the capability of RCPWAVE to predict wave breaking and surf zone wave trans- formation. Model results were compared with data from laboratory experiments. Two sources of data were used. The first source was the original work of Horikawa and Kuo (1966) along with additional information concerning that work found in Dally (1980) and Dally, Dean, and Dalrymple (1984). Horikawa and Kuo studied the transformation of waves in the surf zone using two wave tanks and four different uniform bottom slopes. Two slopes, 1:20 and 1:30, were tested in a wave tank 17 m long and 0.6 m deep. The remaining slopes, 1:65 and 1:80, were tested using a larger tank which measured 75 m in length and 1.2 m in depth. The second source of experimental data was the dissertation work of Izumiya (1984), who used a smaller wave tank for his tests. All water depths considered in the experiments were less than 0.3 m, and all breaking wave data were collected within 7 m of the dry "beach." He investigated wave transfor- mation over three different bottom configurations: a plane beach, a stepped beach, and a barred beach. All slopes were 1:20, including the back slope on the barred beach. 56. Wave and bathymetry conditions for each laboratory test used in the model verification process are shown in Table 2. The table shows the data source, an arbitrarily assigned test case number, the type of beach consid- ered, and the beach slope. The following wave parameters for each test are given also: (a) the wave period, (b) the deepwater wave height (if it were available), (c) the incipient breaking wave height, and (d) the water depth at breaking. 32 Table 2 Summary of Laboratory Data Used to Verify the Wave Breaking Scheme at Hy Ay hy Test Case Bathymetry Slope sec cm _em_ mem Horikawa and Kuo 1 Plane beach 1:20 1.40 -- 13.2 5c Horikawa and Kuo 2 Plane beach 1:30 2.20 -- 9.1 10. Horikawa and Kuo 3 Plane beach 1:30 2.20 -- 12.2 16 Horikawa and Kuo 4 Plane beach 165 56 14.4 Wee 19. Horikawa and Kuo 5 Plane beach 165 1.56 24.7 2 teil 35). Horikawa and Kuo 6 Plane beach 1:80 1.40 -- leet 25 Izumiya 7 Plane beach 1:20 1.19 6.0 Val 9 Izumiya 8 Stepped beach 1:20 0.96 7.9 8.5 9 Izumiya 9 Barred beach 1:20 0.95 6a3 6.9 57. Two series of verification tests were conducted. The first series involved model simulations which were initiated at the break point determined from the data in Table 2. The purpose of these tests was to check the valid- ity of the surf zone transformation part of the breaking scheme. Figures Cl through C6 show plots comparing simulated results with Horikawa and Kuo's data. The horizontal and vertical scales vary from plot to plot. Model re- sults generally show good agreement with observed data. The model tends to underpredict the wave heights very close to shore because the model does not consider the effects of wave setup. Setup would increase the total water depth here and allow for larger simulated wave heights (Dally 1980). Horikaw and Kuo Test 2, having data points 1.0 and 0.5 m from shore, clearly illus- trate this model deficiency. However, neglecting wave setup has little effec on model accuracy in the remainder of the surf zone. Steep slopes, 1:20 and 1:30, produce a much more rapid decrease in wave height across the breaking zone than do the milder slopes, 1:65 and 1:80. Qualitatively, this is what i usually observed in the field. Plunging waves are more likely to occur on steep slopes and spilling breakers on mild slopes. Results suggest that the breaking model is applicable under both types of breaking conditions. 58. Figures C7 through C9 show comparisons between model results and Izumiya's data, again for surf zone transformation only. Test 7, a plane beach case, shows very good agreement. The wave height variation across the 33 wWOnrzA Fon fF FSF WwW a t Ss surf zone is characterized by a strong gradient, typical of steep slopes. Test 8 was conducted using a stepped beach. The model reproduces the same general wave height variation exhibited by the data but not as accurately as in the plane beach cases. The data show a more rapid decay immediately inside the break point, and the decay seems to be toward a stable height less than that predicted by the model. Some oscillations appear in the data, possibly from reflections, which make an estimation of the stable height difficult. The values of « and y used in the model's breaking scheme were selected to provide a "best" fit to both data sets. Better agreement could have been ob- tained for individual data sets by using some other values. There is also evidence that the values of « and y are dependent upon the beach slope (Dally, Dean, and Dalrymple 1984). For simplicity, a constant value for both parameters is used in the model. The final comparison is for the barred beach case. Again, good agreement is obtained for the overall shape of the wave height decay. The model miscalculates the location of the second break point by about 0.3 m, but the simulated decay after this point closely parallels the data. 59. A second series of comparisons, using the same laboratory data, were made. Results from these comparisons are provided to show the capability of the model to simulate the entire shoaling and breaking process, including a determination of the break point. Previously, only the accuracy of the decay mechanism was examined. RCPWAVE was used to simulate wave propagation from generation through to breaking. These simulations were performed for those cases in which the deepwater wave height was given by the authors or could be computed. The deepwater wave height is used as model input. Figure C10 shows the model results from Horikawa and Kuo Test 5. The model could not shoal the wave up to the observed incipient breaking height; however, the simulated surf zone transformation matches well with observed data. 60. Results from similar comparisons between model results and labora- tory data for the Izumiya Tests 7, 8, and 9 are shown in Figures C11 through C13. In all cases the model failed to reproduce the wave shoaling peak imme- diately prior to breaking. The model does decay the wave correctly for Tests 7 and 8. In Test 9 the model misses the first break point entirely. This case was included to illustrate the dependency of accurate surf zone simula- tions on the validity of the incipient breaking criterion used. 61. For the monochromatic wave conditions considered in this 34 verification, and probably narrow-banded spectra as well, the model is inca- pable of predicting the full extent of the shoaling peak prior to breaking, probably due to the use of linear wave theory. This limitation, coupled with any errors in the incipient breaking criterion, may cause the location of the break point to be erroneously specified (e.g., Izumiya Test 9). However, the surf zone transformation part of the model seems to be very accurate for plane beaches and quite reasonable for stepped and barred bathymetry. Consequently, the model is usually capable of simulating the general form of the wave height variation across the breaker zone even though there may be a slight horizontal shift between observed and simulated distributions. This is substantiated by the results presented above. Inclusion of this breaking scheme into the model, despite its shortcomings, is an obvious improvement over methods which specify the surf zone wave height to be proportional to the local water depth everywhere, especially for complex bathymetry involving stepped or barred beaches. The accuracy of this model for use in predicting surf zone charac- teristics under wide-banded spectral wave conditions is questionable. The model assumes wave breaking begins at a well defined point. This assumption is most valid under extremely narrow-banded spectral conditions but is vio- lated otherwise. 35 PART IV: MODEL EXECUTION ON THE CONTROL DATA CORPORATION COMPUTING SYSTEM General Comments 62. The RCPWAVE model can be run in a remote batch mode on the Control Data Corporation (CDC) computing system. Batch jobs comprised of job control language (JCL) allow users to instruct the computer to perform a series of tasks including file manipulation, compilation, and execution. RCPWAVE can be run on two CDC computers, the CYBER 865 and CYBER 205. Costs are less expen- sive on the CYBER 865 machine (cost comparisons will be given in Part V); how- ever, available memory within this computer limits its use to applications in- volving fewer than 9,025 grid cells. The CYBER 205 has more available memory, but it is more expensive to use. It is recommended that users restrict their use of the CYBER 205 to model applications where the total number of grid cells exceeds 9,025. 63. JCL used to run the wave model on the CYBER 865 differs from that used to run it on the CYBER 205. The next two sections explain CYBER 865 JCL and CYBER 205 JCL, respectively. Then the following procedures are explained: submitting batch jobs on both machines, checking job status, and accessing job output. The last two sections give a general description of necessary input files and all output files which are generated in the course of job execution. Part V of the text covers examples of actual applications of RCPWAVE run on both CDC machines, and it includes specific examples of the aforementioned files. 64. It is essential for the user to be familiar with XEDIT* or another text editor available on the CDC system. This knowledge is required in order to make any changes to the JCL files or to examine an output file in a text editor mode. The text editor also is required to create input data files. A limited knowledge of the "UPDATE"* method for making changes to the model source code also is recommended. Discussion concerning modifications to the source code and examples documenting this procedure are given in subsequent sections. * Cybernet services manuals are available from CDC titled "XEDIT, Extended Text Editor," Manual No. 76071000C, and "UPDATE, Version 1 Reference Manual," Manual No. 60449900B. 36 CYBER 865 Job Control Language 65. An example of JCL used to run RCPWAVE on the CYBER 865 is given in Figure 5. The file containing this JCL can be obtained by logging into the CDC computing system and typing GET , RCP865J/UN=CER@Q2 This action will create a local file called RCP865J on the user's work space. In order to save the file permanently, type SAVE, RCP865J Each line or "card image" of RCP865J contains a specific instruction to the computer. Note the brief description of important input and output files un- der the "COMMENT" section. These files will be discussed in greater detail later in Part IV, and specific examples will be given in Part V. At this point, it is only important to know what each file contains. A line-by-line description of the JCL in RCP865J is given in Appendix D. Submitting the CYBER 865 Batch Job 66. A series of commands (JCL) has been assembled into a batch job that instructs the computer to gather input, compile and execute the wave model, and save output. The computer is actually given this batch of commands by using the following form of the SUBMIT command: SUBMIT, ,T The of the file shown in Figure 5 is RCP865J; therefore the following command is given: SUBMIT, RCP865J,T The parameter T tells the computer to return certain output to the user's terminal once the job is completed. When a batch job is submitted, the com- puter responds by giving the job an identifier similar to the one shown below: 15.21.05. SUBMIT COMPLETE. JOBNAME IS AKQBRMA i daqnduiod G9g YAGAD 94 UO AAYMdOY 99Ndex9 09 TOP *PG9QdOU ATTA °G aunsTy 103/ PARARTRIRHRITRI ORK RH IVF DI FRASIAFPRAAPRHIIAAV HSA AAINIG BA Ga KA Ged HHT” LNFLDT * INSWWOD "NOILYWYOANI SOC GSLNOa¥ ONY NOTLWIIdNOI * INAMMOD WONOOMd SHL SO ONILSIT Y ONINIVINOD JTS LNdiNd tidlOddy “LNANWOO se aca iid “INSWHOD SAVIdIH=1' TI SACI (Q3dvL LINN 30IAS0 WIISO7) “NY TadOW SAuM * LNAHWOD : “LIX JHL JO SLWNSSY SHL ONINIVINOD F125 LNdiNO <1NNddIH =“ LNSWWOD i SJAVOdOY “IOV 1d3y * INSKWOD SAGTASIM=T SII SAGO “SINIAI NOLINIXS AGP 40 AMBIC YO JTTSAVO S4Avdddy — “LNSWNOD ; 4503 * NSHWOD INYddD4=945d0 1 $390 1d3Y “C3A0WTY 3a SNK ONY OSYINOSH * INSAWOD Specie ESTEE JON ST JVI4 AMLSWAHLYS 3HL S3S53900 HOIHM 3NI7 *INBWMOS LAL NG 93001 Zire FOP SHL'ATLIDIVAXE NI OY3Y LON ONY 3U4 3ivdgn 3HL * INAWNOO ; NI 3003 NYMIMOS HIM GBLVYSNIS ST AMLSMAHLVE SHI 4] #310Nes © “INSKNOD 34015 SI JM4Avd _ sate 200 eae (Bad¥i JOIAII LINN “WwoI907) * INSWWOOD SAMIADE=1 elite ht AMLAWAHIVE SNINIVINOD FTL4 Wid tLd30dsy — “LNAKWOD 2 1809 * INSUNOD LdLOddy=iNd LNO $30 1dSy (adv) SOIARI LINN WOr8OD “inguWog | G3NOLS Suv SLTNSSY O3LNIYd INdddO4=93d1 FONTS "QSNSTISNOD SOLLSINSLIVYWHD INSWWOD ene ai SSID SU NIA JAM ONY AMLSNO39 MIYS SNTASIIdS FW4 Wivd iWLvddOy “LNAKWOO q31fi93X3 OW 3AtH et * INSWMOD NIg‘d¥O7 "3009 3040S 3HL "INaMMO | Ba oe Sean oe Es genes OL SNOTLWOI4IGOW SNINIVINGD F714 3vod tidendgy ‘uNaWWOQ © | JSG ONT Je 1W314100W ESTEE Ee CU DERE arethie (O=1' 4 SST WM3NEN MS=1) J1¥ddn F : z 2 CSNIVLHO AMLSWAHLYG (MOISE #*FLONe® 335) {dad IN=B3dYL ‘1399 TROON NOTIVS6d04d JAUM 3H YO4 3003 30NNDS and <205 PASSWORD>, respectively), the user's charge information ( and ) with which he/she logged in, and the user's CYBER 865 user number and password (<865 USERNAME> and <865 PASSWORD>, respectively). Once these changes have been made, the JCL file can be submitted with the following command: SUBMIT, AFJCL,T Successful completion of this batch job creates the file AF205 which is re- quired in some of the CYBER 205 commands. 72. An example of JCL used to run RCPWAVE on the CYBER 205 is given in Figure 7. The file containing this JCL can be permanently saved on the user's file space by typing the following commands: GET , RCP205J/UN=CER@Q2 SAVE, RCP205J Ta Jaqnduioo GOZ YAMA 29 UO AAYMdOY 24Ndexe 04 JOr ‘PGOedOe eTTd 103/ ittttisiititiiiiissti tii ititiiititst iit titi titi iit ists tt eM) “LNSKWOD “GOZMSGAD SHL ND LSIX3 LON S300 cidlOddY =" LNSWWOD *INSKWOD (93001 LIND S3IA30 WIISDT) “NNY TSdOW SAM *INSWWOD SHL 30 SLWNSSY SHL ONINIVINOD JIS LAdiNO T=1.M) DO 315 I=1,M DT, J)=-DB(1, J) 315 CONTINUE 60 FORMAT (SX/ (15F8. 2) ) 14 CONTINUE D MAIN. 203 DNULT=10.0 D MAIN.2 PROGRAM RCPWAVE (INPUT OUTPUT TAPE7=TAPE7, TAPES=TAPEG, TAPEG=TAPES *, TAPES=TAPE3) Figure 10. Sample "Update" file for a wave model application 87. The "Update" modification, *D DEPTH.23,DEPTH.26 DO 14 J=1,N READ(8,60) (D(I,J),I=M) DO 315 I=1,M 50 Dera “DCUea) 315 CONTINUE 60 FORMAT(5X/(15F8.2)) 14 CONTINUE and the seven subsequent lines of FORTRAN code delete the statements identi- fied by "DEPTH.23" through "DEPTH.26" in subroutine DEPTH and replace them with the seven new lines. These modifications alter the format used to read bottom bathymetry data; and, since the water depths on the file happen to be negative numbers, a Sign change is programmed into the procedure. The "Update" correction *D MAIN.203 DMULT=10.0 replaces the line in the main program identified by "MAIN.203" with the sub- sequent new line of code. This correction changes the accuracy of the depth matrix in the printed output from whole metres (or other units) to tenths of metres (or other units). As it is written, the model prints out water depths to the nearest whole foot (metre or centimetre), wave heights to the nearest tenth foot (metre or centimetre), and wave angles to the nearest degree. Changes in output accuracy must be made via "Update" corrections. Users are referred to the statements "MAIN.194" through "MAIN.206" in Appendix F for further explanation. 88. These "Update" corrections have illustrated the use of the DELETE (*D) command which deletes line(s) of text. Other frequently used "Update" commands are the INSERT (*I) commmand, which inserts text after a certain line, and the BEFORE (*B) command which inserts text before a line. Users interested in making source code changes should first consult the "Update" manual referenced earlier. Output Files 89. Two permanent output files are generated during the course of model execution on the CYBER 205. These same two files plus one additional file are generated during the course of execution on the front end (CYBER 865). Output file names given in Figure 7 will be used in this discussion. Information contained on the printed output file RCPPRNT is independent of the choice of Dil: machines, but the diary of events RCPDAYF is machine dependent. The file RCPOTPT is generated only by the front-end machine. At some point in the future, RCPOTPT will be generated also by the CYBER 205. 90. The RCPPRNT file summarizes all model input such as grid charac- teristics, wave conditions considered, and bathymetry for that window of the grid mesh defined by the parameters IP1, IP2, INC, JP1, and JP2. For each wave condition simulated, a listing of the following wave characteristics is printed for the two-dimensional field defined by the above parameters: (a) breaker indices defining the location of the surf zone (zeros denote cells where no breaking is occurring), (b) wave angles, (c) wave heights, and (d) the magnitude of the wave phase function gradient (in the absence of ap- preciable diffractive effects this is approximately the wave number, e.g., it is a function of the wave length). Specific examples of this file will not be presented here but rather in Part V, the sample application section. 91. For jobs run on the CYBER 865, a short file (RCPDAYF) is created which summarizes the steps performed during the course of JCL processing. Any errors encountered during compilation and/or execution are indicated on this file. Estimated costs are given also, but these are not the costs which are actually billed to the user's account. Even though this "dayfile" indicates any errors which have caused abnormal job termination, it provides little detail for locating the problem. These details are provided on the file RCPOTPT. 92. This rather large file contains a compiled listing of the model, any compilation errors which may have occurred, and a short variable map. Be- cause of its length, an example is not printed. Any of these output files can be viewed using one of the three methods mentioned previously. It should be noted that the job output returned to the users terminal with the T parameter on the SUBMIT command is very useful and can be viewed using the QGET command. This file contains: (a) the entire RCPDAYF file, (b) actual costs (including the Corps of Engineers discount), and (c) the entire RCPOTPT file. 93. For CYBER 205 model execution the "dayfile," RCPDAYF, contains only those steps actually processed on the front-end CYBER 865 machine. The QGET command must be used to obtain job output from the CYBER 205. This output in- cludes: (a) a file equivalent to the front-end RCPOTPT file (compiled listing and any compilation errors), (b) the diary of events which occurred during CYBER 205 processing, and (c) computer usage and actual cost information. 52 PART V: MODEL APPLICATIONS General Comments 94. General guidance concerning RCPWAVE applications is provided in this section. Two model applications are given to demonstrate the different scales of prototype problems for which the model can be applied successfully. The next two sections explain each example in greater detail. Listings of JCL files used to run each simulation are provided, as are listings of input files and printed output. Comparisons between model execution costs incurred on both CDC computers are given in the last section. 95. Whenever RCPWAVE is a candidate for solving a wave propagation problem, the area of interest is well defined, and wave conditions to be simu- lated are known. The user must create a finite difference grid system encom- passing the area. Grid characteristics determine the success of the applica- tion, so they should be given considerable thought. Two factors completely define the grid, orientation of the axes, and cell resolution. 96. Users should construct the grid system so that the y-axis runs as parallel to the coastline as possible. This causes the x-axis to be directed offshore and probably somewhat perpendicular to the bottom contours. The lat- eral boundary conditions used in the model are most accurate when this axis configuration is adopted. The boundary conditions assume that the variation of the bathymetry, and wave parameters, in the y-direction is small. The as- sumption is most accurate when the y-direction is essentially the longshore direction. Ideally this axis configuration also results in the offshore ba- thymetry having fairly straight and parallel contours and the offshore rows of cells having the greatest depths. The procedure of applying Snell's law to propagate wave information from deep water to the seaward boundary of the model is more accurate if these conditions exist. 97. Waves will generally attempt to advance in directions parallel to the x-axis as a result of the recommended orientation. The model tends to produce erroneous results if computed waves attempt to propagate parallel to the y-axis (wave angles near plus or minus 90 deg). Even with this axis con- figuration, problems may arise due to very irregular bottom bathymetry and/or very oblique wave incidence. These errors manifest themselves via large local Wave angles and occurrences of very large and very small wave heights in 23 alternating cells. An artificial limit on the absolute value of the wave an- gle, 86 deg, is written into the model. Problems of this nature can sometimes -be eliminated by using finer grid resolution. 98. Cell size is the second factor defining the grid system. Accuracy of model solutions computed using finite difference approximations is depen- dent upon cell size; smaller cells result in less error. Diffractive effects can become important on spatial scales with orders of magnitude smaller than the wave lengths being considered. In modeled regions of interest where dif- fraction is important (very complicated bathymetry) cell sizes may need to be some fraction of the wavelength in order to simulate wave propagation accu- rately. Fine resolution is not a requirement for model applications where the bathymetry is very regular. The physical processes of importance, whether it be refraction or a combination of refraction and diffraction, dictate cell sizes which should be used. 99. The examples in the next two sections represent two different kinds of problems. Example I deals with wave propagation over a rather small region with complex bathymetry. Diffraction was presumed to be an important physical process; therefore, finer grid resolution was used in an attempt to represent this effect more accurately. Example II illustrates the applicability of RCPWAVE for propagating waves over a very large area dominated by very regular bathymetry. Assuming that refractive effects would dominate wave transforma- tion throughout the region, cell sizes were increased to a value on the same order of magnitude as the wave length. These two examples show the diversifi- cation of problems which can be addressed using the model. Example I: FRF Pier, Duck, North Carolina 100. Bathymetry in the vicinity of CERC's research pier at Duck, North Carolina, is quite complex as seen in Figures 11 and B2. Figure 11 was plotted using similar bathymetric data digitized onto the rectangular grid system comprised of 75 cells in the offshore (x) direction and 50 cells in the longshore (y) direction. Again, cell sizes are 12 and 24 m in the x- and y-directions, respectively. All depths on the bathymetric file are given in metres below MSL. A constant tidal elevation of 0.90 m is added to the bathymetric data. Two wave conditions are considered: (a) 2-m-deep water wave height, 12-sec wave period, and +20 deg deepwater incident angle (refer 54 Y-AXIS MODEL OUTPUT FOR THIS REGION DUCK PIER, NORTH CAROLINA BATHYMETRY X- AXIS DEPTHS ARE METERS BELOW MSL Figure 11. Bathymetry used in the FRF pier, Duck, North Carolina sample application to the angle convention in Figure 2) and (b) 1.5-m deepwater wave height, 8-sec period, and -35 deg deepwater incident angle. 101. All files associated with this example are listed in Appendix G. Files are arranged in the following sequence: a. JCL file to run this application on the CYBER 865, DUCK865 (Figure G1) b. JCL file to run this application on the CYBER 205, DUCK205 (Figure G2) ec. Input data file , DUCKDAT (Figure G3) d. Source code correction file for the CYBER 865 run, DUCKUPD (Figure G4) e. Source code correction file for the CYBER 205 run, DUCKUP2 (Figure G5) 22 f. A sample of the bathymetric data file , DUCKDEP (Figure G6) g. Printed output file , RCPPRNT (Figure G7) Two-dimensional fields of total water depth, breaker index, wave angle, wave height, and wave number (more precisely, the wave phase gradient) are printed for a portion of the grid extending from rows I=1 to I=50 and from columns J=11 to J=41. Figure 11 shows the extent of this region relative to the en- tire grid system. Example II: Homer Spit, Alaska 102. Bathymetry for this application (see Figure 12) is digitized onto a grid with 96 rows in the offshore (x) direction and 83 cells in the longshore (y) direction. Cell dimensions are approximately 417 ft in the x-direction and 833 ft in the y-direction (about 10 times the resolution used in the Duck, North Carolina, examples. One wave condition is considered in Y AXIS SS “4 7 2 ‘4 MODEL OUTPUT F FOR THIS REGION u 15 20 1 SCALE = oO 1MI “a 15 AG 40 AGE aga i : wl X AXIS HOMER SPIT, ALASKA BATHYMETRY y DEPTHS ARE FATHOMS BELOW MLLW Figure 12. Bathymetry used in the Homer Spit, Alaska, sample application 56 the simulation. The deepwater wave height is 8 ft, the period is 10 sec, and the deepwater wave angle is -45 deg (see Figure 2 for the wave angle conven- tion). Bathymetry is given in fathoms below mean low water so depths are con- verted to feet via a correction to the source code. No water level datum ad- justment is applied. 103. All files associated with this example are listed in Appendix H. Files are arranged in the following sequence: a. JCL file to run this application on the CYBER 865, HOMR865 (Figure H1) b. JCL file to run this application on the CYBER 205, HOMR205 (Figure H2) ec. Input data file , HOMRDAT (Figure H3) d. Source code correction file for the CYBER 865 run, HOMRUPD (Figure H4) e. Source code correction file for the CYBER 205 run, HOMRUP2 (Figure H5) f. A sample of the bathymetric data file , HOMRDEP (Figure H6) g. Printed output file , RCPPRNT (Figure H7) Two-dimensional fields of water depth and wave parameters are given also in Appendix H for the subgrid region denoted in Figure 12. Cost Comparisons 104. The following tabulation shows cost comparisons between simula- tions run on both CDC machines. Costs in dollars are shown for Examples I and II which represent the FRF pier and Homer Spit, respectively. CYBER 865 CYBER 205 Priority Cost _ in Dollars Cost in Dollars Example I Py 2.24 6.09 P3 0.86 4.74 P2 Oni 1.68 Example II PY 2051 6.40 P3 0.96 4.98 P2 0.19 Bed Dilh These are actual costs to the user and include the Corps' fiscal year 1985 (FY 85) discount of 45 percent. Example I was run on a 75 by 50 grid. Two wave conditions were simulated. One wave condition was considered in Exam- ple II, but the grid was larger, 96 by 83. 105. The CYBER 865 is a cheaper, easier computer to work on. It does have central memory limitations. Comparisons show that costs incurred during simulations using the CYBER 205 are not excessive. Users should not sacrifice modeling accuracy simply to avoid using the CYBER 205. 58 PART VI: GRID INTERPOLATION PROGRAM (INTPRCP) General Comments 106. Bathymetry at every cell of the finite difference grid mesh is re- quired as input into RCPWAVE. Since digitization of bathymetric data from survey or nautical charts is both tedious and time consuming, it is desirable to limit the number of times one must perform this task. The grid interpola- tion program INTPRCP provides a method for determining bathymetry on a "new" grid using depth data from an "old" grid. The origin of the new grid can be rotated and/or translated relative to the old grid origin. This capability for interpolation ensures that the bulk of the digitization is done only once. The program is useful when: a. A coarse grid containing bathymetry is available but finer resolution is desired or required. b. The axis orientation of the available grid is different from the desired orientation. c. The region to be modeled is a subset of the available grid. A compiled listing of the program is given in Appendix I. 107. The program uses a fairly simple interpolational scheme. For each new grid cell, a search is done for the nearest old depth value in each of the four 90 deg quadrants relative to the new cell center. A weighted average of these four values is used to compute a new depth. The weighting functions are based on relative distances from the new grid center to the cell centers de- fining the positions of the four old depth values. 108. JCL is available to run the program on the CDC CYBER 205 machine only. The next section briefly describes the procedures performed in the course of job execution. It also explains how an interpolational job is sub- mitted. The third section documents, in detail, all required input files and includes some examples. It also describes the output files created during program execution. A complete example illustrating the use of INTPRCP is presented in the last section. Executing INTPRCP on the CDC Computing System 109. The interpolation program is run on the CYBER 205 machine in a 29 remote batch mode just like the wave model. This machine was chosen instead of the CYBER 865 because it has more available central memory. As a result, users are not limited by the number of grid cells contained in either the old or new grids. A CYBER 205 user number and password must be obtained be- fore attempting to run INTPRCP. The direct access file AF205, mentioned in Part IV, must exist on the user's file space. This file contains validation information for the user's CYBER 205 and CYBER 865 accounts. Refer to Part IV for details concerning these requirements. 110. The JCL file called INTRCPJ, used to run INTPRCP, is shown in Fig- ure 13. A copy of this file can be obtained by logging into the CDC computing system and typing GET , INTRCPJ/UN=CEROQ2 This action creates a local file called INTRCPJ on the user's work space. To save the file permanently, type the following command: SAVE, INTRCPJ The JCL file for executing the interpolation program on the CYBER 205 must first pass through the front-end machine. The first section of JCL commands deals with compilation of the program on the front end and the subsequent re- lay to the CYBER 205. Commands in the CYBER 205 JCL instruct the computer to gather old and new grid information, retrieve bathymetry data for the old grid, compile and execute the program, and save the new grid bathymetry. The "COMMENT" section of the JCL briefly describes required input data files and output files generated in the course of program execution. Before submitting this JCL file, the user must make a few changes. Users must replace the "<205 USERNAME>," "<205 PASSWORD>," and "" with the passwords and user numbers associated with their account. 111. The front-end machine is given the entire batch of commands con- tained in INTRCPJ by using the SUBMIT command in the following way: SUBMIT, INTRCPJ,T The T parameter instructs the computer to return certain output to the user's terminal. The procedure for checking job status and accessing output is iden- tical to that presented in Part IV. No further discussion addressing these points is given. 60 auTYyORU GOZ YAGAD 249 uo ‘ureusoud uoTzeToOduequt 2uq ‘dOYdINI e4noexe 09 Tor ‘fdOUINI ETT 103/ PFT ECIOCSUCrrereirivirrerrereeersereereeleserceetiserevelsc tre reer emenie| |b) “INAWWOS “GINSAI NOTLNTAXS AO’ 40 AMVIM YO FUSAVG AMUdINT =“ LNAWWOD * LNSMWO3 (@3d¥1 JTARG LINN W180) “ENFKWOD ASLBWAHLUG MSN 40 3314 LGN = Nd30INI = “LNSMWOD “INSKWOD (93d¥1 LINN SDIA30 WAIST) “WYYSOYd NOTLYIOdYSLNI “INSHNOD SHL 40 SLWNSSY SH SNINIVINOD JVid LNdiNO = z Ss © u 40 8 OCT 17, 1982 1200 GMT = GAGE #620 © 30 th SIGNIFICANT HEIGHT = 1.42 M PEAK PERIOD = 6.87 SEC 20 10 (0) 0 0.05 0.1 0.15 0.20 0.25 0.30 0.35 FREQUENCY, HZ OCT 25, 1982 1900 GMT GAGE #620 SIGNIFICANT HEIGHT = 2.88 M PEAK PERIOD = 12.34 SEC 2000 GMT = 620 SIGNIFICANT HEIGHT = 2.74 M PEAK PERIOD = 12.34 SEC 0.25 0.30 0.35 FREQUENCY, HZ Figure B1. Observed offshore wave spectra during field verification, Cases 1 through 6 B2 Y-AXIS OCT 16, 1982 BATHYMETRY CONTOURS ARE GIVEN IN METERS BELOW MEAN SEA LEVEL DISTORTED SCALE xX - AXIS Y-AXIS PIER OCT 27, 1982 BATHYMETRY CONTOURS ARE GIVEN IN METERS BELOW MEAN SEA LEVEL ee ah ln UE DISTORTED SCALE nn = X- AXIS ASS Figure B2. Bathymetry around the FRF pier measured on 16 October 1982 and 27 October 1982 2.50 2.00 1.50 1.00 oreo) CASE 1 OCT 13,1982 1300 GMT > 0 = =E oO a = 2.00 lu > << = 5 150 th oO i Z LEGEND = 1.00 n —— RCP WAVE MODEL RESULTS & OBSERVED DATA 0.50 CASE 2 OCT 13, 1982 1400 GMT 0 1.00 0.50 CASE 3 OCT 15, 1982. 1210 GMT 0 50 150 250 350 450 550 650 DISTANCE OFFSHORE, M Figure B3. Comparisons between model results and observed data for field verification, Cases 1, 2, and 3 BY SIGNIFICANT WAVE HEIGHT, M 2.00 1.50 1.00 0.50 CASE 4 OCT 17,1982 1200 GMT 2.50 2.00 1.00 CASE § 0.50 OCT 25,1982 1900 GMT 2.50 2.00 1.50 LEGEND — = RCP WAVE MODEL RESULTS & OBSERVED DATA 1.00 CASE 6 0.50 OCT 25,1982 2000 GMT 50 150 250 350 450 550 650 DISTANCE OFFSHORE, M Figure B4. Comparisons between model results and observed data for field verification, Cases 4, 5, and 6 B5 APPENDIX C: VERIFICATION OF MODEL RESULTS USING BREAKING WAVE DATA COLLECTED IN LABORATORY EXPERIMENTS WAVE HEIGHT (CM) 13 + Ne ak 12 ft a ae Beat 10 7 "seer Q + ye 8 + el 7 + weenie | 6 se 5 ee | 4 ON | a 3 A = 2 Sa 1 a g =z -4 { oO = -6 | =x --12 + ao B16 | 20 | () SO 188 158 200 250 300 350 DISTANCE OFFSHORE (CM) LEGEND arate RCPWAVE MODEL » oe EXPER IMENTAL DAA HORIKAWA LAB TEST 1 ____ BOTTOM PROFILE (BREAK POINT MATCH) Figure C1. Comparisons between model results and observed data for wave breaking verification, Test 1 (surf zone transformation only) WAVE HEIGHT (CM) b + = o SSS Sap Oat Wiens 0 ued Ge miNag his toe meeiiec: TQ hipaa cs Tree ay nn TT Se aun Cine LCI CU fr) ure ey, 0 tre IRS Hina y een y Mie SPE areca am nose al ret VM ire Pn a Sy CT SOR MSS Pr SOREN Rigel aril Remmi Pegg rne o-12+ 1S+ at — —____—+—__— + — iY) 100 158 200 250 300 350 DISTANCE OFFSHORE (CM) LEGEND ee RCPWAVE MODEL Sele Xe RIMeENTAGe DATA HORIKAWA LAB TEST 2 222 BOOM) PROAIWE (BREAK POINT MATCH) Figure C2. Comparisons between model results and ob- served data for wave breaking verification, Test 2 (surf zone transformation only) C2 WAVE HEIGHT (CM) DEPTH (CM) tS 7 4 trent De + ga tt Le = 10 ee. | BiG ee | i oe = reall bee) 1 ra] a ers + uw 6 tT ee + cd i) 7 + a 7 WW et = 2 a Lat | S S47 Bae 4 2] + ae + J if eae af 2 = Sean Oe cee eee ch { ON Ra ce tke, = tu NO tan 7,00) | CMa a MeLLOMET aa eae Siar een | SE fee Pie erie egy atont <0 Chay die Ma aeeseeiete ty PAMINTI PS eee me SRM RIE he MEST cj WON LMMAMM TNC Oust age 1) WON Met pees eek t ay Ah SRO cae au a ye a-16 =e { -20 . ‘ ' ' ah —s Bail 8a 168 2408 320 400 480 56a DISTANCE OFFSHORE (CM) LEGEND _._._. RCPWAVE MODEL .... EXPERIMENTAL DATA HORIKAWA LAB TEST 3 SSS BOmMMPAPRORTIEE (BREAK POINT MATCH) Figure C3. Comparisons between model results and ob- served data for wave breaking verification, Test 3 (surf zone transformation only) - ——— + SS N ~ $$$ _-—$_—}-_— + — 4} a, 12 fF wa af, 18 ye ae af - | it i eet + ee 4¢t + ns 2+ one 9 = Soon ih) oe | SICt ea nt Mata "yn ha) Oh ap ee mene { STUSH CAPE ic Wousisetineneteh Ma a clic ane ig pO eae rear a | pal ais 4 SIs) + +—— + —— 4 @ 280 406 606 82a 1800 1208 1408 DISTANCE OFFSHORE (CM) LEGEND ae REEWAVEsMODEE ~o.. EXPERIMENTAL DATA HORIKAWA LAB TEST 4 2S (BOOM RO re ts (BREAK POINT MATCH) Figure C4. Comparisons between model results and ob- served data for wave breaking verification, Test 4 (surf zone transformation only) C3 WAVE HEIGHT (CM) DEPTH (CM) WAVE HEIGHT (CM) DEPTH (CM) @ 420 820 1200 1680 2020 2400 DISTANCE OFFSHORE (CM) LEGEND = REP WAVER MODEL 2... EXPERIMENTAL DATA HORIKAWA LAB TEST 5 iS BOON PRO hole e (BREAK POINT MATCH) Figure C5. Comparisons between model results and ob- served data for wave breaking verification, Test 5 (surf zone transformation only) a ph | 4 N 28 35 + : @ 300 600 928 1208 1588 1828 2180 DISTANCE OFFSHORE (CM) LEGEND aoe, RCPWAVE MODEL +... EXPERIMENTAL DATA HORIKAWA LAB TEST 6 Bata BOTTOM PROF ILE (BREAK POINT MATCH) Figure C6. Comparisons between model results and ob- served data for wave breaking verification, Test 6 (surf zone transformation only) cy WAVE HEIGHT (CM) DEPTH (CM) WAVE HEIGHT (CM) DEPTH (CM) 30 6a 98 120 150 188 2 DISTANCE OFFSHORE (CM) LEGEND —— RCPWAVE MODEL oo) aeXRERIMENTAGDATA IZUMIYA LAB TEST 7 SSS ST BOMMOMGRRORTEE (BREAK POINT MATCH) Figure C7. Comparisons between model results and ob- served data for wave breaking verification, Test 7 (surf zone transformation only) () 6G 128 180 248 380 360 420 DISTANCE OFFSHORE (CM) LEGEND —..._. RCPWAVE MODEL 22 EXRERINENTALS DATA IZUMLYA LAB TEST 6& ___ BOTTOM PROF ILE (BREAK POINT MATCH) Figure C8. Comparisons between model results and ob- served data for wave breaking verification, Test 8 (surf zone transformation only) C5 + ———— _—$——$—$—————— + + 8 t i | Zot, yy, 4 7 & | Ay | = Sine a— I & ST be -- ea acne es ————— See 4 ‘a ye fe Sn 0 88 bic & Qisar ‘Ja 2 | iv Ea + iS oy is | u WE | $ 2 Powe va | 1 Pe Wf ea: 8 a a 544 Se ee Sls) a ag _ - aa ee o =e a a ~ -16 — —__—+ @ 6a 128 180 248 300 368 420 DISTANCE OFFSHORE (CM) LEGEND gaa as RCPWAVE MODEL ~+.+ EXPERIMENTAL DATA PZUMIY AVE ABR MESTieeS ees BOOMER RO EE (BREAK POINT MATCH) Figure C9. Comparisons between model results and ob- served data for wave breaking verification, Test 9 (surf zone transformation only) WAVE HEIGHT (CM) > ~ + + ——+ + @ 800 1600 2488 3200 4800 4800 S680 OISTANCE OFFSHORE (CM) LEGEND —._... RCPWAVE MODEL -..-. EXPERIMENTAL DATA HORIKAWA LAB TEST 5 22) BOMOMSPRORTNEE Figure C10. Comparisons between model results and ob- served data for wave breaking verification, Test 5 (incipient breaking and surf zone transformation) C6 WAVE HEIGHT (CM) b DEPTH (CM) N + 90 160 270 360 450 540 638 DISTANCE OFFSHORE (CM) LEGEND eS RCPWAVE MODEL as EXPERIMENTAL BATA IZUMIYA LAB TEST 7 BOTTOM PROF ILE Figure C11. Comparisons between model results and ob- served data for wave breaking verification, Test 7 (incipient breaking and surf zone transformation) WAVE HEIGHT (CM) DEPTH (CM) + - + ae + | * 1080 288 300 400 580 600 788 DISTANCE OFFSHORE (CM) LEGEND oS RERWAVE MODEL .+.-. EXPERIMENTAL DATA LZUM EVA EABS TES 6 oS — SO mIOMPROR TIE Figure C12. Comparisons between model results and ob- served data for wave breaking verification, Test 8 (incipient breaking and surf zone transformation) C7 WAVE HEIGHT (CM) DEPTH (CM) D -30 — + + @ 188 200 308 402 S88 600 786 DISTANCE OFFSHORE (CM) LEGEND eae RCPWAVE MODEL 2 +++ EXPERIMENTAL DATA IZUMIYA LAB TEST 9 BOTTOM PROF ILE Figure C13. Comparisons between model results and ob- served data for wave breaking verification, Test 9 (incipient breaking and surf zone transformation) C8 APPENDIX D: LINE-BY-LINE DESCRIPTION OF JOB CONTROL LANGUAGE FOR EXECUTING RCPWAVE ON THE CYBER 865 COMPUTER (1) (2) (3) (4) / JOB JOB , P3,T1000,CM37000. /USER / CHARGE **Tmportant** The job card tells the computer that this is a batch job. The resource card informs the computer of the priority (P) of the batch job, the execution time (T), and central memory (CM) limits. Guaran- teed Cost/ Response SBU* Priority Meaning Time, hr dollars P1 Weekend <48 0.01 run rr P2 Overnight <24+ 0.01 run P3 Slower than default , PA=<205 PASSWORD>)ADY. RESOURCE( JCAT=P3,TL=2000). The following statements instruct the computer to: Give the CYBER 205 the batch of commands in file SENDJOB. Create a diary of events for this batch job and give the diary a local file name RCPDAYF. Save RCPDAYF as a permanent file. Ifa permanent file RCPDAYF already exists, it will be replaced with this new information. Stop processing information if no errors have occurred. If errors occur prior to reaching the EXIT card, the system jumps to this line then continues downward in what is called "error processing." Processing beyond this point consists of saving the diary file as was done in lines 14 and 15. End of record card. All cards following ecard 19 are part of local file INPUT. The job card tells the computer that this is a batch job. The user card identifies the CYBER 205 user for billing purposes. The resource card informs the computer of the priority (P) and time (TL) of the batch job. Guaran- teed Cost Response SBU* Priority Meaning Time, hr dollars P2 Overnight <244+ 0.08 run P3 Slower than ,FM=KOE, AF=AF205. LINK, GET, TAPE7=RCPDATA/DD=C6 UN= ,FMd=KOE, AF=AF205. LINK, GET , TAPE8=RCPDEPT/DD= C6,UN= ,FM=KOE, AF=AF205. FORTRAN, I=NEWPLUS. LOAD ,ON=GO/6000,L=M205, GRLPALL=. GO. LINK , REPLACE(TAPE6=RCPPRNT/ UN= , FM=KOE, DD=C6, AF=AF205) SUMMARY. VEOK T: SBU account block limit. This is the job execution time limit (in seconds). The charge card identifies the charge being used for the current session and bills that charge account for the batch job. The following statements instruct the computer to: Get the permanent file NEWPLUS from the CYBER 865 user account. AF205 is your direct access file containing validation information. Get the permanent file RCPDATA from the CYBER 865 user account and give it the local file name TAPE7. Get the permanent file RCPDEPT from the CYBER 865 user account and give it the local file name TAPES. Compile the file NEWPLUS. The relocatable LGO by default, and the compiled listing is on local file OUTPUT by default. Load the relocatable binary code. Run the program. Take the information on TAPE6 and save it in the permanent file RCPPRNT. Ifa permanent file RCPPRNT already exists, it will be replaced with this new information. The summary card tells the computer to list out all system usage (i.e., blocks, disks, SBU's) for this batch job. End of file marker. EY APPENDIX F: RCPWAVE PROGRAM LISTING “1TO ON ees Ps PROGRAM RCPWAVE( INPUT, OUTPUT, TAPE7, TAPEG, TAPES, TAFE3) HAIN CRAKAAKKARAARARAKARARKAKARKARKARAARARARRARRRARRARRARRARARRARRARARRARKAAK MAIN C MAIN Ckk NOTE kk ‘TQ’ AND ‘JQ’ DEFINE THE LENGTH OF THE ONE AND TWO HAIN C DIMENSIONAL ARRAYS USED IN THE PROGRAM. ‘IQ’ CORRESPONDS HAIN C TO THE X DIRECTION (ON-OFFSHORE) ANI ‘JQ’ 19 THE Y MAIN C DIRECTION (LONGSHORE : HAIN C MAIN CARKARARAAAAARKARRAARARARARARARRARARARARRARARARARARARARARARRARARARRRARAR MAIN C MAIN C PARAM PARAMETER ( 1Q=95, JQ=95) PARAM C PARAA C MAIN Ckk NOTE *k THE PRODUCT [0 & J@ MUST BE LESS THAN 9025 IF THE AODEL HAIN C AFPLICATION IS TO BE RUN ON THE FRONT END CYBER 863 HAIN C MACHINE. ANYTHING LARGER AUST BE RUN ON THE CYBER 205. MAIN C HAIN CRARAAAKARKARAKKARKARAAKARARRARRARRARARRARRARRAARARARRARKAARRARKARRARKAKK MAIN C HAIN Ckk DEFINITION OF IMPORTANT VARIABLE ARRAYS USED THROUGHOUT THE PROGRAM HAIN C MAIN C 2 - WAVE ANGLE HAIN C SiC =U SINGZ) HAIN C CO - C05(Z) HAIN C H - FUNCTION OF THE WAVE AMPLITULE MAIN C CCG - PRODUCT OF THE WAVE CELERITY AND THE GROUP VELOCITY = HAIN C D - TOTAL WATER DEPTH RELATIVE TO SOME DATUM MAIN C RKA - WAYE NUMBER DEFINED BY THE DISPERSION RELATION MAIN C GRDK - GRADIENT OF THE WAVE PHASE FUNCTION MAIN C XMUC - SCALE FACTOR RELATING REAL SPACE X GRID DISTANCES MAIN C TO MAPPED SPACE X GRID DISTANCES AND DEFINED AT THE MAIN C GRID CENTER MAIN C XMUS - SCALE FACTOR RELATING REAL SPACE X GRID DISTANCES MAIN C TO MAPPED SPACE X GRID DISTANCES ANT DEFINED AT THE AAIN C GRID SIDES MAIN C YMUC - SCALE FACTOR RELATING REAL SPACE y GRID [DISTANCES MAIN C TO MAPPED SPACE i GRID DISTANCES ANI DEFINED AT THE HAIN C GRID CENTER MAIN C YMUS - SCALE FACTOR RELATING REAL SPACE Y GRID [ISTANCES MAIN c TO MAPPED SPACE Y GRID DISTANCES AND DEFINED AT THE AAIN C GRID SIDES MAIN C XX - REAL SPACE X GRID DISTANCES MEASURE! FROM THE GRID SAIN C ORIGIN 10 THE GRID CENTER MAIN C {Y - REAL SPACE Y GRID DISTANCES MEASURED FROM THE GRID AAIN C ORIGIN TO THE GRID CENTER MAIN ( HAIN CAAAKARAKKAARAKARAKAARAARARARKARARRRRERARRARARARRARARARARRARARAARRARARKK HAIN C HAIN Ck DEFINITIONS OF INPUT DATA TO BE READ INTO THE PROGRAM xx MAIN C MAIN C ITITLE - ARRAY CONTAINING THE APFLICATION TITLE (70 MAIN c CHARACTERS OR LESS) MAIN C H - NUMBER OF GRID CELLS IN THE X DIRECTION HAIN C DX - GRID SIZE IN THE X DIRECTION MAIN C N - NUMBER OF GRID CELLS IN THE Y DIRECTION MAIN C DY - GRID SIZE IN THE Y DIRECTION MAIN C kKNOTEAX G - GRAVITATIONAL CONSTANT WHICH DETERMINES THE UNITS OF MAIN 372) Ln 4 oo bo (SS see oe ao 2 QO On ee Oo me Hrd ODO |r Ss — ao tae an to = t2 t2 co bro 24 Coe Jitee). (20 spktsa el clalsr) (re) Creditor (sel Cel tel ese let se) Csr) (se) (se) (oe) tr) ose)-(se J toy) Goedel) is) Gz} C CNTRANG - NCASES DLEVEL ) HDEEP - IDEEP - ZDEEP - LY IP2 INC JFL = IPB ‘ IGKID - AKNOTEAR IREF COMMON/ANGLES/ COMMON/WVH/H(T COMMON/DEPTHS/ COMHON/WAVNUM/ COMHON/ CONST,’ AMN,M1,MZ NAL, COMMON, FRINTC/ COMNON/CONS3/T ALL THE INPUT AND OUTPUT VARIABLES APPROXIMATE ANGLE THE OFFSHORE CONTOURS MAKE WITH THE Y AXIS (AIDS IN A BETTER INITIAL GUESS OF THE SOLUTION COMPUTED USING SNELL’S LAW) NUMBER OF INDIVIDUAL DEEP WATER HEIGHT-PERIOD- DIRECTION CONDITIONS CONSIDERED CONSTANT WATER LEVEL ADDED TO OK SUBTRACTED FROM THE ENTIRE DEFTH MATRIX DEEP WATER WAVE HEIGHT INPUT CONDITIONS DEEP WATER WAVE PERIOD INPUT CONDITIONS DEEP WATER WAVE DIRECTION INPUT CONDITIONS STARTING VALUE OF I FOR THE PRINTED OUTPUT ENDING YALUE OF I FOR THE PRINTED OUTPUT INCREMENT OF I FOR THE PRINTED OUTPUT STARTING VALUE OF J FOR THE PRINTED QUTPUT ENDING VALUE OF J FOR THE PRINTED OUTPUT (THE J INCREMENT 15 ALWAYS 1) =0 IF CONSIDERING A CONSTANT SIZED RECTANGULAR GRID =] IF CONSIDERING A YARIABLY SIZED RECTANGULAR ‘3k 1D GENERATED USING THE MAPIT PROCEDURE IN CMSGRID. FOR ADDITIONAL INFORMATION ABOUT THE YARIABLY SIZED GRID INPUT SEE THE COMMENTS IN ‘SUBROUTINE GRID’ =] DIFFRACTIVE EFFECTS INCLUDED =Q DIFFRACTIVE EFFCTS IGNORED(PURE REFRACTION) KAAKKARKKARAARARAKARARARAARARARRARAAKARRARRERARAARERRRARARAARARRERARRRR Z(10,JQ),S1( 18, JQ) COC 10, JQ) Q,J@) ,CCG( 10. JQ) DC 1G, JQ) RKA(1Q, JQ) ,GRDK (10. JQ) G,P1,P12,RAL,HCONVR,SCONVR DX, DY ,DX2,DY2,7,OMEG, NM2, IWVET, IDRY, IWETP1 CNTRANG,HFACT DLEVEL IP], 1P2, INC, JP1,JP2,DMULT,HMULT, ZMULT, RKMULT GRID, IREF, [TAHX, ITHMX. IDIFF COMMON/MUSC/XMUC (IQ) , XMUS( 10), YMUC( JQ) , YMUS( JQ) COMMON/COOR/XX COMHON /TRANE/ DIMENSION HDEE (TQ) YY (JQ) DECAY ,STABL, IBRK( JQ) , IRRKM( JQ) P(200) , TDEEP(200) ,2DEEP (200) .LTITLE(9) Ckkkkkakh READ INPUT DATA FROM FILE CODE ” C C READ(? 601) (LT 601 FORMAT (9A8) ITLE(L),L=1,9) READ (7, 100)M,DX,N,DY,G,CNTRANG,NCASES , DLEVEL 100 FORMAT(1S,F10. 4,15,F10.4,2F10.2,15,F10.2) DO 602 L=1,NCASES READ(7,103)HDEEP(L) , TDEEP(L) ,ZDEEP(L) 103 FORMAT(3F10.2) 602 CONTINUE READ(7, 101) IFL 101 FORMAT(SI5) »IPd, INC, JP1,JF2 READ(?, 102) IREF, IGRID 102 FORMAT(215) CkkkkAAKK WRITE OUT INPUT DATA ON FILE CODE 6 C WRITE(6,15) 15 FORMAT(/////,2X,/REG TONAL COASTAL’,3X, BS MAIN MAIN MAIN MAIN MAIN HAIN MAIN HAIN MAIN MAIN MAIN HAIN HAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN HAIN HAIN MAIN MAIN MAIN HAIN HAIN MAIN HAIN MAIN MAIN HAIN HAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN HAIN HAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN HAIN MAIN HAIN 113 119 120 lal V2 leg 124 125 126 1a? 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 131 152 153 154 Ni) 156 137 158 159 160 1ol 162 163 164 165 166 167 168 169 170 171 72 173 174 175 176 PROCESSES WAVE TRANSEORMATION, 43X,/M ODE L,/,43X,/0 ROPWAVE)’,////) WRITE(6,609) (LIITLE(L) ,L=1.9) 609 EORMAT(25X,9A8, ///) WRITE(6,55) 55 FORMAT(,’,1X,/MOUEL INPUT:’,//) IE‘ IGRID.GT.0)G0 TO 300 WRITE(6, 41) 4] FORMAT(1X, ‘UNIFORMLY SIZED, RECTILINEAR GRID MESH’.,’) 80 10 301 300 WRITE(6, 42) 42 FORMAT(1X,VARIABLY SIZED, RECTILINEAR GRID MESH’ , /) 301 WRITE(6,5)4,0X,N,DY 5 FORMAT(5X, ‘Y - DIRECTION (ON-OFESHORE)’,5X,1S,’ CELLS, EACH’, KE10.2,’ IN LENGTH’./,5X,’Y - DIRECTION (LONGSHOKE) ’,5X, 15. k’ CELLS, EACH’,E10.2,° IN LENGTH’, /) WRITE‘, 43)6 43 FORMAT(1X, THE ACCELERATION OF GRAVITY IS’,f8.2,’. THESE UNITS ADETERMINE THE UNITS OF ALL INPUT AND OUTPUT VARIABLES ’,,) DO 604 L=1,NCASES WRITE(G,44)L yHUEEP(L) , 1DEEP(L) , 2DEEP(L) 604 CONTINUE 44 EORMAT(’ THE DEEP WATER WAVE PARAMETERS FOR CASE’.13,’ ARE:’, 45X, ‘HEIGHT=’ ,£7.3,5X, ’PERIOD=‘,£7.3,5%, /ANGLE=’ ,£8.3) WRITE (6,45) CNTRANG 45 FORMAT(/,1X, ‘THE OFFSHORE CONTOURS MAKE AN ANGLE OF’ ,E7.2, k’ DEGREES WITH THE Y AxI3’./) WRITE (6, 193 19 FORMAT(1X, THE BATHYMETRY MATRIX IS VARIABLE IN BOTH HORIZONTAL’ k,‘ DIRECTIONS ANI! WAS READ FROM FILE CODE 3’,/) WRITE(5,20)DLEVEL 20 FORMAT(1X,‘A WATER LEVEL CHANGE OF’,F7.2,’ WAS ADDED TO THE’. A’ ENTIRE BATHYMETRY MATRIX’) C Chrkhrkhh CONSTANTS USED IN THE PROGRAM C P1=3.1415927 FIZ=PI &2.0 RaAD=180.0/P1 CNTRANG=CNTRANG/ RAD Ha=M-2 H1=H-1 NM1=N-1 NHQ=N-2 DXE=DXKL. DY2=DYAc. WIA=1.0 WIH=1.0 TAU=0.167 BETA=0.167 IDRY=1 IWET=2 IWETP1=IWET+1 C Ckkkkkkkk ‘STABL’ AND ‘DECAY’ ARE USED IN THE WAVE BREAKING CrkrkkakK ROUTINE C STABL=0.4 DECAY=0.2 FY HAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN HATH MAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN HAIN HAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN HAIN MAIN MAIN HAIN MAIN AAIN MAIN MAIN HAIN MAIN HAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN HAIN HAIN 117 118 119 120 Va eg 123 1234 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 14] 142 143 144 145 146 147 146 149 150 151 lue 153 154 og 15t 15? 15¢ 15) 160 161 16a 163 104 189 166 167 168 169 170 ay es 173 174 ic 79 C ChkRARAAR HCONVR’ AND ‘SCONVR’ ARE THE CONVERGENCE CRITERIA USED IN ChAkARAAA THE HEIGHT AND ANGLE ITERATIVE SOLUTION SCHEMES L HCONVR=0..0005 SCONVR=0.90025 IF(G.G7.9.7.AND.G.LT.9.9)HCONVR=HCONVRAO. 3048 1F(G.G7.979.0, AND. G.LT.990.0)HCONVR=HCONVRA3O. 48 C Cakkakkah ‘ITHMX’ AND ‘TTAMX’ CONTROL THE MAXIMUM NUMBER UF ITERATIONS CkakARKKK ALLOWED IN THE WAVE HEIGHT AND ANGLE SOLUTION SCHEMES Chkkhakak “IDIEF’ CONTROLS THE NUMBER OF ITERATIONS ALLOWED IN THE Craarctah ITERATIVE DIFFRACTION SCHEME C TTHMX=5¢ TTAMX=50 INIFF=15 st L CakakkAAA THE FOLLOWING MULTIPLICATION FACTORS CONTROL THE ACCURACY CAkkAARtA OF THE PRINTED QUIPUT‘NOT THE ACTUAL COMPUTATION). CRAARARRK DEPTH (1) ~ DMULT CARRAKARR WAVE HEIGHT (H) - HMULT CARARAARR WAVE ANGLE (2) - ZMULT ChARRAKKK WAVE NUMBER (GRADK) - RKMULT CkkkARKAK THE VARIABLES ARE FIRST MULTIPLIED BY THE SCALE FACTORS Crkthkakk KELOW, THEN PRINTED QUT IN INTEGER FORM L UMULT=1.9 HAULT=10.6 DMULT=1.9 REMULT=1000.0 C CAkkkaAAR DEFINE THE GRID SCALE FACTORS AND DISTANCES FOR A CONSTANT Charakhhe SIZED RECTANGULAR GRID C 10 2 I=1,4 XMUC(1)=1.0 XAUS(1)=1.0 XX(T)=DX4(1-0.5) 2 CONTINUE 0 3 J=1.¥ (AUC(I)=1.9 YMUStJ)=1.0 WD) =0fACI-9.5) 3 CONTINUE 4 ry i Sy Chkkkhkak CALL SUBROUITNE GRIL TO READ IN THE VARIABLE GRID MAPPING Chkkkkkkk INFORMATION FROM FILE CODE 3 (X DIRECTION FIRST, THEN 1) AND Chakthhkh GENERATE THE VARIARLE GRID SCALE FACTORS AND [DISTANCES C TE(IGRID.EQ.1)CALL GRID U Ckkkkakkh CALL SUBROUTINE DEPTH TO GENERATE THE WATER DEPTH MATKIX C CALL DEPTH C Chkkkkkhkh ADD [LEVEL TO ALL THE WATER DEPTHS AND THEN REQUIKE Chkkkktkk ALL DEPTHS BE GREATER THAN THE MINIMUM DEPTH ‘DMIN’ Ckkkkkake WHERE “DMIN’ IS 1.0 FEET OR A METRIC EQUIVALENT BS MAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN HAIN HAIN HAIN MAIN HAIN MAIN MAIN HAIN MAIN MAIN MAIN HAIN MAIN HAIN MAIN HAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN HAIN MAIN HAIN MAIN HAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN HAIN 236 ake bel au: 238 239 240 24] 242 243 244 245 346 247 348 249 200 aul] ode ad a4 205 2d 207 qc. ad 209 260 261 362 263 264 269 266 267 268 269 17 al a7 oie 273 274 7g aw al a7 273 279 230 281 tJ ao 7 @ on & OO td e bs co DMIN=1.6 1E(G.G7.9.7.AND..LT.9.9) DMIN=0. 2048 1E(G.67.970.0.AND.G.LT.990.0)DHIN=30. 48 DO 87 I=1,4 10 87 J=1,N D(I,J)=0(1, J} #DLEVEL TE(D(1,J).LT.DMIN)D( 1, J)=DMIN 87 CONTINUE G. Chkkkkkth SET THE BOUNDARY CONDITIONS FOR THE WATER DEPTHS C DO 86 I=1,4 D(I,1)=0(1,2) D4 1.N)=D(1,NAL) 86 CONTINUE CALL ONBC(D) c CkkakkkaR PRINT THE TOTAL WATER DEPTH MATRIX ‘ALL DEPTHS MULTIPLIED BY 0 C CALL POUT(IP],IP2,INC,JP1.JP2,’ WATER DEPTHS ",D,DAULT) C Ckkkkkkhk ITERATE OVER THE NUMBER OF WAVE CONDITIONS CONSIDEREL C DO 605 L=1,NCASES HO=HDEEP(L) T=TDEEP(L) OMEG=P 12/T HEACT=2. 0XOHEG/G C Cakkkkakk ‘HEACT’ I5 A FACTOR T9 CONVERT FROM WAVE HEIGHT TO THE CrkkAAKAA AMPLITUDE FUNCTION ‘H’ C A=ZDEEP(L) WRITE(6,606)L 606 FORMAT(////",° WAVE CONDITION’,1,/) WRITE(6,44)L,HO,T,A A=A+180.0 0 507 J=1,N IBRK(J)=0 IBRKH(J)=0 607 CONTINUE CALL REFDIE(A,HO,WIA.TAU.WIH, RETA) 605 CONTINUE 99 STOF END CARAAAKAARAKAKRARARRAARARARAARARKARARRARRAARRRAARRARAR AR ARRARRRARRARRA RA C SUBROUTINE REFDIE(THETAO,HH,WIA, TAU,WIH, BETA? C CRRARARKARAAKEARARKARAAARARRARARARARARERARARRARRARRARRARARAARRRRRARRRR RA C C THIS SUBROUTINE CONTROLS THE ITERATIVE SOLUTION SCHEME AND C PRINTING OF THE WAVE INFORMATION C CARKAAKAARARARARARARAARAAARARKARRARRARRARRARRARRARRARARARRRRAR AR ARARARRR C PARAHETER( I0=95,, JQ=95) F6 MAIN MAIN HAIN HAIN MAIN MAIN MAIN MAIN HAIN HAIN HAIN MAIN MAIN HAIN MAIN MAIN MAIN HAIN AAIN MAIN HAIN HAIN MAIN MAIN HAIN HAIN MAIN HAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN HAIN HAIN HAIN SAIN HAIN MAIN HAIN HAIN MAIN MAIN HAIN MAIN REED KEFDIF REEDIE REFDIE REEDIE REFIVIE REEDIE KEFDIF REEDIF REFDIE PARAH PARAM RE} 236 7) 46 Perle) zag 240 241 ze 243 244 oA5 246 247 24g 249 aril aril 365 ode 259 254 ac ad ac ad 57 ac wd ac wd 260 261 262 263 264 265 266 267 268 269 270 271 475 we 40 a/ 2/4 ard leks Pras aan ul t ay al & ove) 280 281] “2 Oo Of be os he, Wes OO OI) tor] COMMON/ANGLES/2( 10. JQ) ,51(10,JQ) CO’ 12, JQ) COMMON/WVH/H(1,JQ) CCG 10,1) COMMON/ DEPTHS’ 10, JQ: COMMON, WAVNUM/RKA: IQ, JG) GRDK( 10, JQ: COMMON/CONST,’ G, PI, PID, KAL,HCONYR, SCONE, DX, 0Y.0X2 02,1. OMEG, AM N, HL, MO,NM] NMC, IWET, IDRY, IWETFi.CNTRANG HEACT [LEVEL COMMON/PRINTC,/IP1,IP2, INC, JP1,JP2,DMULT HAULT.ZAULT, KKMULT COMHON/CONS2/ IGRID, IREF, ITAMY, ITHAX, IDIFE COMMON /TRANE, DECAY, STABL, [BRK(JQ), IBRKK( JQ) DIMENSION DUMi‘ 10, JQ) ,GREOLD JQ: C CaakARRAA CALL SUBROUTINE SNELL TO OBTAIN AN INITIAL GUESS GF THE CkkaARARK WAVE HEIGHTS AND ANGLES USING SNELLS LAW C CALL SNELL |‘ THETAG,’RAD) HH) CALL ONKC(H) CALL ONBC (2) CALL ONBC(CO: CALL ONBC{51} CALL ONBC(RKA) CALL ONBC(SRDK! CALL ONBC{ CCI) C Crkakkakh REMOVE THE “0 TO i232 STATEMENT TO PRINT OUT THE SNELL’S LAW Carrkkekr SOLUTION C 40 TO 125 177 CONTINUE 00 13 I=1,4 110 13 J=1.N QUHG=2(1,J)-PI DUM (1,J)=DUN3*RAD 12 CONTINUE C Ckakaktak ANGLES HEIGHTS, AND WAVE NUMBERS AXE AULIIPLIED Sy ZMULT. CrkARKAAA HMULT, AND REMULT RESPECTIVELY IN THE FRINT OUT. THESE MUST BE Ckkkkkakk CHANGED INTERNALLY WITHIN THE MAIN FROGRAM Ir OTHER ‘ALUES Cakakrare ARE DESIRED CALL POUT(IFL,IPS,INC,JPL,JPo,’ WAVE ANGLES = (DEG »DUHL, «ZMULT: 1G 79 I=1,é 10 73 J=1.N DUAL 1.5)=H¢ 1,3) xHEACT 79 CONTINUE CALL POUT(IP1,IP2,INC,JP1,JP2,’ WAVE HEIGHTS * DUM1, 1HAULT} CALL POUT(IP1,IP2,INC,JF1,JFo,’ WAVE NUMBER ' RRA, ARKMULT) 122 CONTINUE C CrkkkaARK ROW BY ROW MARCHING LOOP c DO 10 IL=H2, IWETP1,-1 ILH1=IL-1 C Ckkkkkakk COMPUTE THE WAVE ANGLES ALONG A ROW C F7 PARA REFDIF REFDIE REEDIF REFLIF KEEL IF REEDIE KEFIVIF KEFDIE REFDIF REELIE REED IEF REELIE REFD iF REEDIF REFIIIE REEDIE REFLUE REFDIE REFDIF REFDIF KEFDIF REEDIE REFIIE REEDIE REFDIF REFLDIE REEDIF REEDIE KEFDIE REELUIEF REFDIE REFDIE REFINE REFLIE REFLIE REFDIE REFLUIE REEDIE REFDIF KEFDIE XEFDIF REEDIE REFLIIEF REELIE REFDIF KEEDIF REFDIE FEFDIE REEDIE REFDIE REFLIIF REEDIE REFIUIF KEFDIE KEFDIF REFDIE KEEDIF REEDIE or CN ote CIC MiP CnEenvensenPen rc ci woo ™“M CALL ANGLE(IL, IL, ITAHX,WIA, TAU, SCONVR) C Chkkkkakkk COMPUTE THE WAVE HEIGHTS ALONG A ROW C CALL HEIGHT (IL, IL, ITHAX,WIH, BETA,HCONVR) C TE( IREF.EQ.0) GO 10 114 DO 119 J=1,N GRDOLD(J)=GRDK( ILH1, J) 119 CONTINUE DO 110 LLL=1, IDIEF C Ckrkkkkkk COMPUTE NEW GRADIENT OF THE WAVE PHASE FUNCTION ALONG A ROW C CALL GRADK( ILH1, ILM1) EPSK=0.95 DO 112 J=1,N GRDK ( ILM], J)=EPSKAGRDK ( ILM), J)+(1.0-EPSK) AGRDOLD( J) 112 CONTINUE TFLAG=1 HO 111 J=1,N TE(ABS(GRDK ( ILM1,J)-GRIGLD(J)) .GT.0.00254ABS(GRDK ( ILK1,J))) kIFLAG=0 111 CONTINUE {0 113 J=1,N GRDOLD (J) =GRDK( ILM1,J) 113 CONTINUE C Cakkkakkk RECOMPUTE THE WAVE ANGLES ALONG A ROW C CALL ANGLE(IL, IL, ITAMX,WIA, (TAUAL.0) ,SCONVR) C Ckkkakkth RECOMPUTE THE WAVE HEIGHTS ALONG A ROW C CALL HEIGHT( IL, IL, ITHMX,WIH, (BETAX1.0) ,HCONVR) TE(TELAG.EQ.1) GO TO 114 110 CONTINUE WRITE(6,117) ILA] 117 FORMAT(1X, ‘CONVERGENCE TOWARD A SOLUTION FAILED ON ROW’, I3) 114 CONTINUE C Crkkrrkkh UPDATE BREAKER INDEX C BO 115 J=1,N IBRKM(J)=IBRK( J) DUM1( ILH1,J)=IBRK(J) IBRK(J)=0 115 CONTINUE C 10 CONTINUE CALL ONBC(GRDK) CALL ONBC(H) CALL ONBC(Z) CALL ONBC(CO) CALL ONBC(SI) C Crrkkkakk PRINT WAVE INFORMATION C Chkkkkkkk BREAKER INDEX ( O=NON-BREAKING , 11=BREAKING ) F8 REFDIE REEDIF REEDIF REEDIF REFDIE REFDIF REFDIF REEDIF REFDIF REED IE REFDIF REFDIF REED IF REEDIF REEDIF REEDIE REEDIF REFDIE REFDIEF REFDIF REFDIF REEDIF REFDIF REFDIE REFDIF REEDIE REEDIF REEDIF REFDIEF REEDIE REED IF REED IEF REFDIF REEDIE REFDIF REEDIF REFDIF REFDIF REFDIE REEDIE REEDIF REEDIE REFDIE REEDIE REFDIE REFDIF REFDIF REFDIF REFDIE REEDIE REEDIF REELIE REFDIE REFDIF REFDIE REFDIF REFDIF REEDIF REFDIE sao On > Wb Nn w co DO 219 J=1,N DUM) (1, J)=DUML(2, J) DUMI(M,J)=0.0 DUAL (M1,J)=0.0 DUML(H2,J)=0.0 DO 219 I=1,4 TE(DUMI (I,J) .EQ.1.0)DUMI(I,J)=11.0 219 CONTINUE CALL POUT(IP1,IP2,INC,JP1,JP2,’ BREAKER INDEX “,DUM1,1.0) CrxaKKARA ANGLES HEIGHTS, AND WAVE NUMBERS ARE MULTIPLIED BY ZMULT, CarkaARRAK HMULT, AND RKMULT RESPECTIVELY IN THE PRINT OUT. THESE MUST Crkkkkkkk BE CHANGED INTERNALLY WITHIN THE MAIN PROGRAM IF OTHER VALUES Chkkkhkhk ARE DESIRED c DO 23 I=1,H DO 23 J=1,N DUM=2(1,J)-PI DUM] ( 1, J)=DUMSARAD 23 CONTINUE CALL POUT(IP1,IP2, INC,JP1,JP2,’ WAVE ANGLES © (DEG)’,DUML, AZMULT) C Ckkkkkkkh CONVERT EROM AMPLITUDE FUNCTION TO WAVE HEIGHT C DO 81 I=1,4 DO 81 J=1,N DUML(I,Ji=H( I,J) AHEACT 81 CONTINUE CALL POUT(IP1,IP2,INC,JP1,JP2,’ WAVE HEIGHTS ’ DUM, 1HMULT) CALL POUT(IP1,IP2, INC, JP1.JP2,’ 4AVE NUMBER ’ GRDK, ARKMULT) 99. RETURN END CRARAAKAKARKAAKARAAAAAARARARARAAAAARAARARRAARARRARRARARAARRARRARRRAARRRR C SUBROUTINE GRADK( ISTART, TEND) C CARAKAARAKARARAARAAKARARAAARARAARRARAARARKARAARARARAARRARERARRRRAAARARRKK C Cc THIS SUBROUTINE COMPUTES THE UPDATED VALUES OF THE GRADIENT C OF THE WAVE PHASE FUNCTION ALONG A GIVEN ROW c CAARARARAAARAAAARARRARKARKARRARAAAAARARARAARARARRARARRARRARRRARARRARK ARK C PARAMETER ( 10=95, JQ=95) C COMMON/ANGLES/Z(1G,J@).S1(1G,JQ) ,CO( I,J) COMMON/DEPTHS/D( 1G, JQ) COHMON/WVH/H( 18, JQ) ,CCG( 18, JQ) COMMON/WAVNUHM/RKA( TQ, JQ) ,GRDK( 10, JQ) COMMON/CONST/ G,PI,PI2,RAD,HCONVR,SCONVR,DX,DY,DX2,D¥2,T,0MEG, AM N,H1,M2,NM1,NM2, IWET, IDRY, IWETP],CNTRANG , HEACT, DLEVEL COMMON/CONS2/IGRID, IREF, ITAHX, ITHMX, IDIFE COMMON/MUSC/XMUC( 1), XMUS( TQ) , YMUC( JQ) , YMUS (JQ) COMMON /TRANE/ DECAY,STABL, IBRK( JQ), IBRKM(JQ) DIMENSION DUM1(10,JQ) ,x(JQ) Eg REFDIE REFDIE REFDIE REFDIE REFDIF REFDIE REEDIE REFDIF KEEDIE REFDIE REFDIE REED IEF REEDIE REFDIEF REFDIF REFDIF REEDIF REFLIIF REEDIF REFDIE REEDIF REFDIE REEDIE REEDIF REED IF REFDIF REEDIF REEDIF REFDIF REEDIF REFDIE KEFDIEF REFDIE REFDIE REEDIF GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK PARAM PARAM PARAM GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK “1 Oo Cn & OF 2 me Be worse Ow wo — & Co eee “10 cn se woo ty to brs [oe od to Ckxkkkkkk COMPUTE THE DIFFRACTIVE TERMS C Crkkakkkk USE 4 POINT BACKWARDS DIFFERENCE FOR THE X CURVATURE OF ’H’ Chkkkkkkk USE 3 POINT BACKWARDS DIFFERENCE FOR THE % GRADIENT OF ‘H,CCG’ Chkkkakkk USE CENTRAL DIFFERENCES FOR THE { CURVATURE OF ‘H’ Chkkkakkk USE CENTRAL DIFFERENCES FOR THE Y GRADIENT OF ’H,CCG’ C DO 2 I=ISTART, TEND DLX2=DX2AXHUC (1) DLXSO=(DLX240.9) AK2 DO S J=2,NM1 DLY2=DY24YKUC (J) DLYSQ=(DLY240.5) xk2 CCGIJ=CCG(1, J) HIJ=H(1,J) HIPI=H(1, J+1) HJM1=H(1,J-1) HIPI=H(I+1,J' HIPZ=H(1+2,J) DUM6=(-3.04H1I+4. OAHIP1-HIP2) /DLX2 DUM4=1 2. 0AHII-5. OAHIP1 +4. OAH IP2-H( I+3, 1) )/DLXSQ DUM4=DUM4-0.. SADUMGA (XMUC( I+] )-XMUC(I-1) )/((XMUC( 1) kk2) KDX) DUA2=(-3. 0aCCGII+4. OACCG( 1+], J)-CCG( +2.) )/DLX2 DUM7=(HJP1-HIM1) /DLY2 DUMS=(HIP1-2.0AHII+HJM1) /DLYSO DUMS=DUMS-0. SADUM7&( YMUC ( J+1)-YMUC(J-1))/( (YMUC(J) &&2) ALY) DUM3=(CCG(1,J+1)-CCG(1,J-1))/DLY2 DUM1 (1, J)=(DUR4+DURS+ ( DUM2ADUM6+DUM3ADUM7 ) /CCG IJ) /HIJ = CONTINUE C Ckkkkkkkk CHECK FOR POINT TO POINT OSCILLATIONS IN WAVE PHASE GRADIENT C 10 410 I=ISTART, IEND DUM1(1,1)=DUM1( 1,2) (WMI (1.N)=DUM1 (1, NAL) SKU=4.¢ SBETA=0. 25 10 409 J=1,N X(J)=DUAL(I.J) 409 CONTINUE 0 408 J=3.NM2 DUMZ=ABS(X(J+1)-X(J)) DUAS=ABS(X(J)-X(J-1)) DUM4=ABS (X(J+1)-X(J-1) 40.5 TF ((DUM2+DUM3) LT. (SMUADUM4) GO TO 408 DUMS=X(J+1)-2.0aX(J)+X(J-1) DUMG=X{1+2)-2.0AX(J+1)+X(J) DUM7=X(J)-2.04X(J-1)+X(J-2) TE( (DUMSADUHG) .GE.0.0.AND. (DUMSADUM7) .GE.0.0)G0 T0 408 DUM1 (1, J)=X(J)+SBETAA(X(J+1)-2.0AX(J)+X(J-1)) 408 CONTINUE 410 CONTINUE DO 17 I=ISTART, TEND DO 17 J=2,NH1 Ckkkkkkkk DO NOT INCLUDE DIFFRACTIVE EFFECTS INSIDE OR IMMEDIATELY CkkkkkARK ADJACENT TO THE BREAKER ZONE c F10 GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRALK GRADK GRADK GRADK GRADK GRADE GRADK GRADK GRADK GRADK GRALIK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK GRADK Cc “Sam ON eS IBTEST=IBRKA( J-1)+IBRKM(J)+IBRKM(J+1)+IBRK(J-1)+IBRK(J)+ GRADK IBRK(J+#1) GRADK IE(IBTEST.GT.0) G0 0 17 GRADK c GRADK CxarkAKKK LIMIT THE CHANGE IN THE GRADIENT OF THE WAVE PHASE FUNCTION GRADK Carkkakkk FROM THE DISPERSION RELATION WAVE NUMBER TO 50 PERCENT GRADK c GRADK RKOLD=RKA( I,J) GRADK RKADD=0. 254RKOLD GRADK RKARG=RKOLDA42+DUM1 (1, J) GRADK TE (RKARG.LE.0.0) RKARG=( (OMEGAA2/G) &42) GRADK RKNEW=SQRT(RKARG) GRADK RKD TFF=RKNEW-RKOLD GRADK TF(ABS(RKDIFF) .LT.(0.0025ARKOLD) G0 TO 17 GRADK TE(ABS(RKDIFE) .LE.RKADD)GO TO 341 GRADK TE(RKDIFE.LT.0.0) RKNEW=RKOLD-RKADD GRADK TE(REDIFE.GE.0.0) RKNEW=RKOLD+RKADD GRADK 341 GRDK(1,J)=RKNEW GRADK 17 CONTINUE GRADE C GRADK Cxrkkkkkk SET LATERAL BOUNDARY CONDITIONS FOR THE GRADIENT OF THE WAVE SGRADK Cakkakkak PHASE FUNCTION GRADK C GRADK DO 38 I=ISTART, TEND GRADK GRDK(1,1)=GRDK(I,2) SRADK GRDK(1,H)=GRBK( 1,1) GRADK 38 CONTINUE GRADK RETURN GRADK END GRADK Cakkkrhrakkararaahakrkraarkrrerkhaaraarka akan kariaaakkkkkkek HEIGHT C HEIGHT SUBROUTINE HEIGHT( ISTART, IEND, ITMAX,WI,ALPHA,HCNY) HEIGHT C HEIGHT Carkarkrrrraraeraak kkhnhakankaaararakaahhakhkikkakekeakkrekkk HEIGHT Cc HEIGHT c THIS SUBROUTINE ITERATES TO SOLVE FOR THE WAVE HEIGHTS HEIGHT C ALONG A GIVEN ROW HEIGHT Cc HEIGHT Cakkacarknakertachinkrcrararancrgnrragrkaaaakrekaaerharkerakrrkkahe HEIGHT Cc PARAM PARAMETER ( [0=95, JQ=95) PARAK C PARAM COMMON/ANGLES/Z( 10, JG) ,$1(10,J@) ,CO(1G,J&) HEIGHT - COMMON/WVH/H(10,J@) ,CCG( 1G, JQ) HEIGHT COMMON/DEPTHS/D(1@,J@) HEIGHT COMMON/WAVNUM/RKA( 10, JQ) ,GRDK( 19,10) HE IGHT COMMON/CONST/ G,P1,P12,RAD,HCONVK,SCONVK,DX,DY,DX2,DY2,7,OMEG, HEIGHT xM,H,M1,42,WM1,NM2, IWET, IDRY, IWETP1, CHTRANG,HEACT, DLEVEL HEIGHT COMMON/CONS2/IGRID, IREF , ITAMX, ITHMX, IDIFF HEIGHT COMMON/MUSC/XMUC( IQ), XHUS(1Q), YHUC( JQ) , YRUS(JQ) HEIGHT COMMON/COOR/XX(1@) , Y¥(J@) HEIGHT COMMON /TRANE/ DECAY,STABL, IBRK(J@) , IBRKM(J@) HEIGHT DIMENSION DM8(JQ) ,SLOPE(JG) HEIGHT Cc HE IGHT Ckkdckhth SOLVE DIFFERENCED FORM OF CONSERVATION OF WAVE ACTION EQUATION HEIGHT Cc HEIGHT DO 500 I=IEND, ISTART,-1 HEIGHT IM=I-1 HE IGHT DO 450 IT=1, ITHAX HEIGHT Fi1 wo CO 8 OY oe CO bo a) ~~ o MOM WWW WW WO WW Ww Wo Wf Ys PI ft MH PS be DO 200 J=2,NM1 JP=J+1 JM=J-1 DML=CCG( 1M, JP) AGRDK( IM, JP) ASI( IK, JP) DM2=CCG( IM, JM) AGRDK( IM, JM) ASI( TH, JM) DAS=CCG(1, JP) AGRDK (1, JP) ASI(1, JF) DM4=CCG(1, JK) AGRDK( 1, JH) ASI(1, JM) DMG=(WTA(DM1AH( TH, JP) AA2-DMZAH( TH, JH) kA) = /(DY2AYMUC()))+((1.0-WT)A(DMSKH( 1, JP) AX2-DM Ak = H(T, JM) 4x2) /(DY2KYMUC( J) )) DML=(COG( 1, J) AGRDK(1,J)ACO(1, J) )ACH(T, J) AH (I,J) ) DM2=(CCG(1,JK)AGRDK(1,JK)ACO(1, JM) )A(H(1, JM) AH(1, JK) ) DM3=(CCG( 1, JP) AGRDK( 1, JP)ACO(1, JP) )ACH( 1, IP) AH( 1, IP) ) DM4=CCG( IM, J) AGRDK( IM, J) ACO( IM, J) DMS=( (DMG) A(DXAXMUS( IM) ) +ALPHAADH2+ e (1.0-2. OXALPHA) ADH] +ALPHAADH3) /DM4 C ChxkkAAKK CONVERT AMPLITUDE FUNCTION TO WAVE HEIGHT C DM7=DMSA(HEACTAHEACT ) C Chkkkkkkk CHECK FOR WAVE HEIGHTS LESS THAN ZERO C IE(DM? .LT.0.00001) DH7=0.00001 DM7=SQRT(DM7) C Ckkkkkakk CHECK FOR WAVE BREAKING OR WAVE TRANSFORMATION C IF(DM7 .GT.STABLAD(IH,J)) THEN C Crkakkkkk CALCULATE ANGLES AND CELLS OF INFLUENCE c THETA=Z(1M,J)-PI IF(THETA.GE.0.) THEN 410.54 (XX (IM) +XX( 1) )-XX( TH) XQ=XX(1)-XX (1M) Y1=YY(J+1)-YY (1) Y2=0 OA(YY (J) 4Y¥ (J#1) )-¥¥ (J) ANG1=ATAN2(Y1,X1) ANG2=ATAN2(Y2,X2) IE(THETA.GT.ANGL) THEN KEY=IBRK(J+1) IKEY=IH JKEY=J+1 ELSE IF(THETA.GT.ANG2) THEN KEY=IBRKM(J+1) IKEY=1 IKEY=J+1 ELSE KEY=IBRKM( J) IKEY=1 JKEY=J END IE ELSE X3=XX(1)-XX( 1M) Fl2 HE IGHT HE IGHT HEIGHT HEIGHT HE TIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HE TIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT mr bb FO bo bb BO BD BD Bt ee res ere tI EI YYW WWW wor hp rotors C X4=0 GR (XX (THK) +XX( 1) )-XX (1M) Y3=0..5A(YY (J) +¥¥(J-1))-1Y (J) Y4=Y¥(J-1)-YY(J) ANG3=ATAN2 (13, X3) ANG4=ATAN2(Y4,X4) TE(THETA.GT.ANG3) THEN KEY=IBRKM( J) IKEY=] IKEY=J ELSE IE(THETA.GT.ANG4) THEN KEY=IBRKM(J-1) IKEY=1I JKEY=J-1 ELSE KEY=IBRK(J-1) IKEY=I¥ JKEY=J-1 END IE ENDIF CrkkkkkKR COMPUTE INCIPIENT BREAKING WAVE HEIGHT USING METHOD FROM CrrkkkAAK THE SHORE PROTECTION MANUAL (WEGGEL’S EMPIRICAL METHOD) C C Jd=(J+(IKEY-J-1)/2) DIST=SQRT( (FLOAT ( IKEY- IM) ADXAXMUS( IM) ) AAZ+ (FLOAT (JKEY-J) ADYAYMUS (JJ) ) x42) SLOPE (J)=(D( IKEY , JKEY)-D( 1M,J))/DIST SLOPE (J)=AMAX1(0.0,SLOPE(J)) HS IG=1. OADH7 Al=43.754(1.0-EXP(-19.0xSLOPE(J)) ) Bl=1.96/(1.0+EXP(-19. S4SLOPE(]) )) DEPBRK=HS1G/(B1-(A1 AHS 1G/(GATAT) ) ) IF(DEPBRK.GT.D(IK,J)) KEY=1 CkARKKAKA CHECK WHETHER TO ACTUALLY TRANSFORM WAVE C C C C IF(KEY.EQ.1) THEN IBRK(J)=1 DM1=0.3k(D( IKEY, JKEY)+D( 1H, J)) DM2=CCG( IKEY , JKEY )AGRDK ( TREY, JREY) AC H( IKEY , JREY ) Ax2- (STABLAD( IKEY , JKEY)/HEACT) Ak2)-CCG( TH, J) AGRDK( IH, J)’ (STABLAD( IM, J)/HEACT) Axo DMS=DXAXHUS (1M) ADECAY,/(2. OADM DMA ) DMS=(DMS+DMSADH2)/(1.0-CCG( IM, J) AGRDK( 1K, J) ADM3) DM7=DMSx (HEACTAHEACT ) TE(DM7 LT. ((STABLAD( IH, J) )Ak2)) DN7=(STABLAD( IM, J) ) 4x2 DM7=SQRT (D7) ENDIE DAG (1) =D47 Ckkkakirr CHECK FOR WAVE HEIGHT CONVERGENCE C DO 400 J=2,NM1 Eg HEIGHT HE IGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HE IGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HE IGHT HEIGHT woo 047=048 (J) HH2=H( IM, J) AHEACT C Crkkkkkkk UPDATE THE WAVE HEIGHT C EPSZ=0.9 DA7=EPSZADM7+(1.0-EPSZ) kHH2 SUM=SUMK+ABS ( DA7-HH2 ) C Carkaxkkk CONVERT HEIGHT BACK TO AMPLITUDE FUNCTION C H(IM,J)=DH7/HEACT 400 CONTINUE C Crkkkkkkk SET LATERAL BOUNDARY CONDITIONS FOR WAVE HEIGHT C H(TM,1)=H(IM,2) H(IM,N)=H( IK, NM1) C Crkraakkk TEST FOR CONVERGENCE C TE(SUM.LT. (ELOAT(NH2) AHCNV)) GO TO 500 450 CONTINUE ¢ IF(IREF.EQ.1)G0 TO 500 WRITE(6,475) IM 473 FORMAT(1X, ‘RELAXATION FOR WAVE HEIGHTS FAILED ON ROW =’, 14) C 500 CONTINUE RETURN END pvyerevercecyecevirusccrcercvryeceryersrrerververervrrerercerecceryr tse! c SUBROUTINE SNELL (THETAO,HH) c errrcoceererierrreccrrrrrererrerirrrrcrrrerirrrrerert rete rr rere rites C C THIS SUBROUTINE COMPUTES THE SNELLS LAW SOLUTION OVER THE ENTIRE C GRID C Ciacci kod dadicdddicdacaic oda ddd dk C PARAMETER( 10=95, J0=95) C COMMON/ANGLES/Z( 10, JQ) ,$1(10,J0) ,CO( 10, JQ) COMMON/WVH/H( 10, JQ) ,CCG( 10, JQ) COMMON/DEPTHS/D\ 10, J0) COMMON/WAVNUM/RKA( 10, JQ) ,GRDK( 12, JQ) COMMON/CONST/ G,P1,P12,RAD,HCONVR, SCONVR, DX,DY,DX2,DY2,1,0HEG. AM,N,M1,H2,NMl jNH2, IET, IDRY, IETP],CNTRANG,HEACT, DLEVEL COMMON/PRINTC/IP1, IP2, INC, JP1,JP2,DMULT, HMULT, ZMULT, RKNULT COMMON/CONS2/IGRID, IREF, ITAX, ITHAX, ID IEE c Crrkakkrkk COMPUTE THE WAVE NUMBERS USING THE PADE APPROXIMATION Chkkkkkkh (SEE THE COASTAL ENGINEERING NOTEBOOK) c DO 1 I=IWET,H DO 1 J=1,N DD=D(1,J) F14 HE IGHT HEIGHT HE IGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT HEIGHT HE IGHT HEIGHT HEIGHT SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL PARAM PARAH PARA SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL DUMI=(OMEGAK2) ADD/G DUM2=DUM1+1.0/(1.0+0. 65224DUM1 +0. 46224 K(DUK1AX2) +0. 08644 ( DUM A44)+0.06794 (DUM AAS) ) DUMS=TASQRT (GADD/DUM2 ) RKNUM=P 12/DUM3 RKA( I,J) =RKNUM GRDK(1,J)=RKNUM C Carkkkakk COMPUTE THE HEIGHTS AND ANGLES USING SNELL’S LAW Cikarkakk COMPUTE SIGMA AND CCG C DUM1=RKNUMADD DUM2=2. OADUM] DUM3=TANH (DUML ) DUM4=S INH (DUM2) SINE=S IN (THETAO-CNTRANG) ADUM3 ZANG=P I-ASIN(S INE) +CNTRANG 2(1,J)=ZANG SI(I,J)=SIN(ZANG) CO(I,J)=COS(ZANG) DUHS=SQRT (COS ( THETAO-CNTRANG) /COS ( ZANG-CNTRANG) ) H(T,J)=HHADUMSASQRT(0.9/(0.5%(1.0+DUN2/DUM4) AKDUM3) ) COG(T,J)=0.54(1.0+(DUM2/DUM4) ) \ OMEGAR2) / A(RKNUMAK2) 1 CONTINUE C Cakkrkakk CHECK FOR WAVE BREAKING C DO 600 I=IWET,M DO 604 J=1,N DUAS=H(1, J} HBRK=0.78AD(1,J) TE(DUMS.GE.HBRK) DUHS=HBRK C CAARARAARCONVERT HEIGHTS TO AMPLITUDE FUNCTION (HAG/2x5 IGNA) C H(1,J)=DUMS/HEACT 604 CONTINUE 600 CONTINUE RETURN END CAARRAARARAKRARARAARARAARARAARARRARRAARARRARRARRARARARARARRKARARKARAREARK C SUBROUTINE ANGLE( ISTART, IEND, ITMAX,WT,ALFHA, SCNV) C CAAKAAKAKKARKARAAKARAAARKARRARAARARAAARARARARARRARRARRARRARAARARARARAR AK C C THIS SUBROUTINE ITERATES TO SOLVE FOR THE WAVE ANGLES C ALONG A GIVEN ROW C CARRAKAAARAKARKARARARARARARARARARRKAARARRARAARAARAARARARARARRARARRRAR ARK C PARAMETER( [Q=95,, JQ=95) C COMMON/ANGLES/7Z(1Q, JQ) ,S1(10,JQ) .CO{ 10, JQ) COMMON/DEPTHS/D( 1a, JQ) COMMON/WAVNUM/RKA( 10, JQ) ,GRDK( 10, JQ) COMMON/CONST/ G,PI,P12,RAD,HCONVR, SCONVR,DX,DY,DX2,DY2,1,OMEG, Fal\5 SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SHELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL SNELL ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE PARAM PARAM PARAM ANGLE ANGLE ANGLE ANGLE — ee wor OW DWI CW & Wr le ed OO > Oo kM,N,M1,M2,NM1,NM2, IWET, IDRY, IWETP1 ,CNTRANG,HEACT, DLEVEL COMMON/CONS2/IGRID, IREE, ITAMX, ITHAX, IDIFE COMMON/MUSC/XMUC (IQ), XMUS( TQ), YAUC( JQ) , YMUS (JQ) DIMENSION DUM1( 10, JQ) ,X(JQ) C CrkkAAAAK SOLVE THE [IEFERENCED FORM OF THE IRROTATIONALITY OF THE Ckkkkkkkk GRADIENT OF THE WAVE PHASE FUNCTION EQUATION C DO 1 I=IEND, ISTART,-1 IM=I-1 LO 4 IT=1, ITHAX DO 2 J=2,NM1 DUMG=ALPHAA(GRDK( 1, J+1)&S1(1,J+1)) k +(1.0-2. OAALPHA) A(GRDK(1,J)4S1(1,J)) k +ALFHAA(GRDK (1,J-1)AS1(T,J-1)) DUM2=WTA(GRDK(I-1,J+1)ACO( I-1,J+1)-GRDK(I-1,J-1)A RCO(I-1,J-1))/(DY2AYHUC (I) ) k +(1.0-WT) ACGRDK (1, J+1)4CO( 1, J+1)-GROK(1,J-1)% RCO(I, J-1))/(DY2RYMUC (I) ) TIUMS=DUMG- (DXAXMUS ( T-1) ) ADUN2 DUM4=DUM3/GRDK< 1-1, J) DUM1(1,J)=DUM4 2 CONTINUE SUK=0.0 BO 22 J=2,NHl DUM4=DUM1(1, J) DWHS=Z( 1-1, J) DUK3=S IN(DUMS ) C CkkkkAKKA UPDATE THE SINES C EPSZ=0.9 DUM4=EPSZADUMA+( 1. 0-EPSZ) ADUMS C Cakkkkhkk LIMIT OBLIQUE WAVE ANGLES C IF(DUM4.GE.0.997) DUM4=0.997 TE(DUM4 .LE.-0.997) DUM4=-0.997 DUM6=P 1-AS IN(DUMA4) SUM=SUM+ABS ( DUM6-Z( IK, J) ) 2(1M,J)=DUM6 SI(IM, J)=DUM4 CO‘ 1M, J)=COS(DUMG) 22 CONTINUE G ChakARAAA SET LATERAL BOUNDARY CONDITIONS FOR WAVE ANGLES ,SINES,AND Carkakrkk COSINES C Z(H, 1)=Z( 1M, 2) CO(IM,1)=CO( IK, 2) SIC IM,1)=S1( IM, 2) Z(TK,N)=Z( IM, NM1) CO(1M,N)=CO¢ IM, NM1) SICIM,N)=S1( IM, NHL) C ChkkkAAAK CHECK FOR ANGLE CONVERGENCE C TE(SUM.LT. (NM2ASCNV) )G0 TO 1 4 CONTINUE F16 ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE ANGLE co a) C3f) tw 8 et. 3 a OU & tw BI et 63 m0 On “1D ON B&B ww PS wow IE(IREE.EQ.1)G0 TO 1 ANGLE WRITE(6,643) IM ANGLE 643 FORMAT(1X, ‘RELAXATION FOR WAVE ANGLES FAILED ON ROW =’, 14) ANGLE 1 CONTINUE ANGLE 99 RETURN ANGLE END ANGLE CRARAAKARAARARAARARARARARARRARRARAAAARARARRARRRARRARRARARAAARAAAARAAKARK DEPTH C DEPTH SUBROUTINE DEPTH DEPTH C DEPTH CAAAAKAKAAAAAAAAKARAAAARAAAARARARARRARAAARARRARARAAARAARRARAKARARKARRAKK DEPTH C DEPTH C THIS SUBROUTINE GENERATES THE WATER DEPTH MATRIX DEPTH C DEPTH CAKAAAAAARAAKARAARARAARAKAARARARRARARARARRARARRAARRARARRKRARAARAAAAARAAK DEPTH C PARAM PARAMETER ( 1Q=95, JQ=95) PARAM C PARAM COMMON/DEPTHS/D( IQ, JQ) DEPTH COMMON/CONST/ G,P1,P12,RAD,HCONVR, SCONVR,DX,DY,DX2,0Y2,1,0MEG, DEPTH AM,N,M1,M2,NM1,NM2, IWET, IDRY, IWETP1,CNTRANG,HEACT, DLEVEL DEPTH COMMON/CONS2/IGRID, IREF, ITAMX, ITHMX, IDIFE DEPTH COMMON/MUSC/XMUC (IQ) ,XMUS( 1), YMUC (JQ), YHUS(JQ) DEPTH COMMON/COOR/XX (10), YY(JQ) DEPTH C DEPTH CAkAKAKKK READ IN VARIABLE BATHYMETRY FROM FILE CODE 38. FIRST READ DEPTH CAkRAAAAK IN THE ’ALONGSHORE’ ROW CLOSEST TO SHORE, THEN PROCEED DEPTH CrkRAKKAK ROW BY ROW IN THE OFFSHORE DIRECTION DEPTH C DEPTH DO 14 I=1,4 DEPTH READ(8,90)(D(1,J),J=1,N) DEPTH 14 CONTINUE DEPTH 30 EORMAT(10F8.2) [TEPTH 99 RETURN DEPTH END DEPTH CARARKARAARARARARARARARARARARRRARRARARARARARARARKKAKKARKKARKARRKARARARAAR POUT C POUT SUBROUTINE POUT(II1, 112, IYAL, JSTART, JEND, ITITLE, DUM1,FACT) POUT C POUT CARAKAAAARARKAAAKARARARARARARRARARARARARKARAAARARARARARARRARRRRRARARRARKA POUT Ct POUT C THIS SUBROUTINE PRINTS OUT SELECTED VALUES OF A PARTICULAR ARRAY POUT C ,DUM1, WHICH ARE SCALED BY THE VALUE OF ‘FACT’ POUT c POUT CARRAARRAARARARAAARARRARARARARARRRARARARRARAARARAARARARRRARRARRRARRARARR POUT C PARAM PARAMETER( IQ=95, JQ=95) PARAM C PARAM COMMON/CONST/ G,PI,PI2,RAD,HCONVR, SCONVR,DX,DY,DX2,D¥2,1,QMEG, POUT AM,N,H1,H2,NM1,NM2, IWET, IDRY, IWETP1 CNTRANG,HEACT , DLEVEL POUT COMMON/CONS2/ IGRID, IREF, ITAMX, ITHMX, IDIFE POUT INTEGER IX(JO+31), ITITLE(3) POUT DIMENSION DUM1( 18, JQ) POUT C POUT NC=31 POUT WRITE(6, 100) ITITLE, FACT POUT 100 FORMAT(///,3A10,5X, ‘(MULTIPLIED BY ’,F6.0,’)’) POUT J1=ISTART POUT J2=ISTART+NC-1 POUT Balig, — worn & wy OO Dro CH Sm w to — ad wre OW aI ON S&S wt = CRARKARAARKAKARKARRARAARARKARAARARRARARRARAARRARRARRARAARARRRARARRRRRRRK c on oOonrgATAagaAM NaN YONI YOINMG Onl aN Soa Aaa am a 1 IF(J2.GI.JEND) J2=JEND WRITE(6,102)(J,J=J1,J2) 102 FORMAT(/,3X,’I/J:‘,3114) WRITE(6,103) 103 FORMAT(1X, k 1 eee ee - - - - - - - e - - - - -- - = = - = k 1 en nee enon saa owen My DO 2 I=L, 112, IVAL DO 3 J=J1,J2 RND=0.9 IF(DUM1(1,J).LT.0.0)RND=-0.5 3 IX(J)=INT( EACTADUM] (1,J)+RND) 2 WRITE(6,104) 1, (1X(J),J=J1,J2) 104 FORMAT(1X,13,2X,‘:’,3114) J1=J1+NC J2=J2+NC IF(J1.LE.JEND)GO TO 1 WRITE(6,101) 101 FORMAT(//) RETURN END SUBROUTINE GRID THIS SUBROUTINE READS THE VARIABLE GRID MAPPING INFORMATION FROM AAKARKKARAKARKARRAAKAARARARRARRARARARRRRARRARARRARRARRRARRERRRARRRRRRKR FILE CODE 3 (X REGION FIRST, THEN Y) AND GENERATES THE VARIABLE GRID SCALE FACTORS ANI! DISTANCES TQ THE GRID CENTERS WHEN GENERATING A VARIABLY SIZED GRID IT IS RECCOMENDED THAT THE MAPPING BE DONE IN MAP INCEHES FROM SOME BATHYMETRIC CHART OF A KNOWN SCALE. THE ‘DX’ AND ‘DY’ USED AS INPUT INTO THE MODEL ARE THEN SIMPLY THE NUMBER OF FEET OR METERS PER MAP INCH. IF MAP INCHES ARE NOT USED IN THE MAPPING, THE VALUES OF ‘XSCALE’ AND ‘YSCALE’ CAN BE SET 10 SOMETHING OTHER THAN 1.0 (IN CONJUNCTION WITH THE CHOICE OF ‘DX’ AND ‘DY’) TO CONVERT FROM THE MAPPELI SPACE INTO REAL SPACE KARKARAKARKARAARRAARARRRARARRARARARARARRARARRARARARARARARAARARARARARARKA ARDEFINITIONS OF VARIABLE GRID MAPPING INPUT REQUIRED BY THE MODEL NREG(X,Y) - IS THE NUMBER OF MAPPING REGIONS IN THE X OR Y DIRECTION NA(X,Y) - IS THE NUMBER OF GRID CELLS IN A PARTICULAR MAPPING REGION IN THE X OR Y DIRECTION A(X, Y)pB(X,%) ,C(X,¥) - ARE THE MAPPING COEFFICIENTS FOR A PARTICULAR REGION IN THE X OR Y DIRECTION PARAMETER ( IQ=95, JQ=95) KAKARKAARKAARARARRARRAARAARARARRARARRARRARARRARARRARAARRARRARRRRRARRRRR COMMON/CONST/ G,PI,P12,RAD,HCONVR,SCONVR,DX,DY,DX2,DY2,1,OHEG, AM,N,HL,M2,NML,NH2, IWET, IDRY, IWETP1,CNTRANG,HEACT, DLEVEL COMMON/CONS2/IGRID, IREF , ITAMX, ITHAX, IDIEE COMMON/HUSC/XMUC( TQ), XMUS( TQ), YMUC( JQ). YHUS( JQ) F18 POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT POUT GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GR ID GRID GRID GRID PARAM PARAM PARAM GRID GRID GRID GRID 10 C Caarrkarkk READ MAPPING INFORMATION C C CAkkARKAA WRITE THE VARIABLE GRID INFORMATION ON FILE CODE 6 C COMMON/COOR/XX( TQ), YY (JQ) DIMENSION AX(50),BX (50) ,CX (SO) .NAX(S0) DIMENSION AY(50),BY(50) ,CY(50) NAY (50) CHARACTERA] SIR XSCALE=1.0 YSCALE=1.0 I=] I=] 2] CONTINUE READ(3,31,END=999) STR,NST,NEND,Al,B1,C1 31 FORMAT(AL,7X,218,3016.11) NEND=NEND-1 IE(STR.EQ.’Y’) GO TO 20 AX(1)=Al BX(1)=1 CX(1)=C1 DO 201 LLC=NST,NEND LL=LLC+1 ALPHC=LL-0.5 ALPHS=LL XMUS (LL-1)=(B1AC1A(ALPHSAR(C1-1.0)) )AXSCALE XMUC(LL-1)=(BIAC1A(ALPHCAR(C1-1.0)) )AXSCALE XX(LL-1)=(AL+B1A(ALPHCAACI ) )AXSCALEALX 201 CONTINUE NAX(1)=NENI+1-NST NXREG=1 I=I+1 G0 TO 21 20 CONTINUE AY(J)=Al BY(J)=B1 CY¥(J)=C1 10 203 LLC=NST,NEND LL=LLC+1 ALPHC=LL-0.5 ALPHS=LL YMUS (LL-1)=(BIACLA(ALPHSAA(C1-1.0))) AYSCALE YHUC (LL-1)=(B1AC1&(ALPHCAR(C1-1.0)) }&YSCALE YY(LL-1)=(A1+B1A(ALPHCAACL ) ) AYSCALEALY 203 CONTINUE NAY (J) =NEND+1-NST 999 CONTINUE WRITE(6,9) 9 EORMAT(////,20X, VARIABLE WAVE GRID INFORMATION’ ,///) WRITE(G,23) XSCALE, YSCALE 23 EORMAT(///, EXPANSION COEFFICIENT SCALE FACTORS’./, k’XSCALE=’ ,F10.3,0X, ‘ YSCALE=’ ,F10.3,//) WRITE(6,9) 5 FORMAT(1X,°X EXPANSION COEFS(A,B,C) AND GRIDS PER REGION’ ,//) F19 GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID aomncancnan on cn cn ca woo G® cn & OI fa 98 99 100 101 102 102 104 105 106 107 108 109 110 11] 112 113 114 115 116 117 118 ee ee omow jt @ on ee W& fe iP) ta eee an & jw mee ies oa! 19 =) ti £2 C. bo is] jw S) t WRITE(6,4)¢1,AX(1) BACT) ,CX(1) ,MAX(1), I=1,NXREG) GRID 4 FORMAT(110,3E20.7, 110) GRID WRITE(6,6) GRID 6 FORMAT(///,1X,’Y EXPANSION COEFS(A,B,C) AND GRIDS PER REGION’,//) GRID WRITE(6,4)(1,AY(1),BY(1) CY(1) MAY (1), I=1,NYREG) GRID WRITE(6,7) GRID 7 FORMAT(///,1X,’X SCALE FACTORS (XMUC,XMUS)’,//) GRID WRITE(6,2)(1,XMUC( I) ,XMUS(I), I=1,H) GRID WRITE(6,8) GRID ® EORMAT(///,1X,’Y SCALE FACTORS (YMUC,YHUS)’,//’) GRID WRITE(6,2)(1,YMUC(1), YMUS( 1), I=1,N) GRID 2 FORMAT(S(15,2F10.9)) GRID WRITE(6,10) GRID 10 FORMAT(///,1X,‘X CENTER DISTANCES’ ,//} GRID WRITE(6,11)(1,XX(1),1=1,4) GRID 11 FORMAT(8(14,F12.3)) GRID WRITE(6,12) GRID 12 FORMAT(///,1X,’Y CENTER DISTANCES’ ,//) Gk ID WRITE(G,11)(1,YY¥(J),J=1,N) GRID RETURN GRID END GRID CARAKARAAARARARAAARAAAKARAR RARAAAARARAARARRARARARARARARRARRARRRARRRARAKK ONBC C ONBC SUBROUTINE ONBC(DUM1) ONBC C ONBC CARARAAAKARRAAKARARARAAARARRARARAARARRRRARARARARAAAAKAARAARAARRARARKARKK ONBC C ONBC C THIS SUBROUTINE SETS THE ONSHORE BOUNDARY CONDITION . ONBC C THIS BOUNDARY CONDITION IS NOT USED IN THE COMPUTATIONAL SCHEME ONBC C SINCE IT PROCEEDS FROM OFFSHORE TOWARDS ONSHORE. ONBC c ONEC CARRARAARAAAAAAAARARARAAAARAAAARARRRARRARARRARARARAAARAARKAARARAARAARARR ONBC C PARAM PARAMETER ( 10=95, JQ=95) PARAM C PARAM COMMON/CONST/ G,PI,P12,RAD,HCONVR,SCONVR DX ,DY,DX2,DY2,1,OMEG, ONBC AHN ML M2,NM1.NM2, IWET, DRY, IWETP ,CNTRANG HFACT, DLEVEL ONBC COMMON/CONS2/ IGRID, IREF, ITAMX, ITHAX, IDIFE ONBC DIMENSION DUM1( 10, JQ) ONEC 0 1 I=1, IDRY ONBC DO 1 J=1.N ONBC TWH1(1,J)=DUM] (IWET, J) ONBC 1 CONTINUE NEC RETURN ONEC END ONBC F20 oO APPENDIX G: SAMPLE FILES--FIELD RESEARCH FACILITY PIER, DUCK, NORTH CAROLINA, WAVE PROPAGATION EXAMPLE G9QMONC 103/ 209999990999909999999990999990999909909099090999999999009990909099 ° NIKO) * INSRWOD "NOLLYWMOANI 80f GAL¥ody ONY NOLL ITdROO * INSWHOOD WYMOONd SHL 30 SNIISIT ¥ SNINIVINGD F114 LNdLNO s1dlOddY =“ LNGKHOD * INJOD (93dv1 LINN JOIA3S0 WIISOT) “NOY TS00H SAvM * INSWOD SHL JO S1WIS3Y FHL ONINIVINGD F1I4 LNd NO = LNddY |“ LNSWHOD * LNAI “SINSAS NOILNISX3 Of 30 AWVIG YO SISA +SAVOdDY =“ LNSHOD * INS “CGAOWSY 34 LSM CNY CIYINoFy * INS LON SI S114 AMLSWAHLYG SHL S3SS3090 HOTHM 3NIT * INO WOE SHL‘ATLIIINdX3 NI Gv3Y LON ONY F114 alvdd) FHL “NSA NI 3009 NVULYOS HLIM CALVYSN3S SI AMLSWAHIVG SHL 4] s8310Nes =“ LNAKIOD (B3dvL SOAS LINN W180) * LN3WAOD AMLSHAHIVE SNINIVINGD F114 VLU = =d300Nd “LN3KWOD * LNIOD (Zad¥i SOIA3d LINN WII907) * LNSWWOD *CSMS0ISNOD SOTLSTMALOVuHO * LNFWWOD JAM ONY AMLSWO39 C18 ONTASIIIdS JUS WING s1¥0XONd = *LNSHWOO * LNA "3000 SOuNdS FHL * NSH OL SNOILVDISIOOW SNINIVINGD JWI4 FiVddA -d¢NXONd =“ LNSWAOD * N30 “TR00H NOTLVS¥d0Ud SAM 3H. 403 3003 3040S <3AMdIY = “LNSKOD * INSHHOD 299902989990909990990999899990999099990909000090902999990809090000" NBO) #* INSMIOD (Jar) JS¥NSNY1 TOMLNOS @0f SAGE SHL *° INSANOD A@ C3YINGIY SIVW4 SNINYZINGD SINSWHOO 9° INDO) 899999990999929099099999959090990000099999000099902990099999990008 "NBD "TD oanst dy * SAUTdIU ‘SOW 1d * AAMID TUE TSI SAV *LIXd * SAGO dDY ‘SWS * SAMO INET TTL SAGO "1509 * INBddU=I3IdUL ‘SIV TTY * LdLOdTH= INA LO § 301d * LNGLAO ‘93d0 1 ‘ONT MSY *LIX3 * dABOdIY ‘SIVAN “AAMT IN=1 STI SAVT *1s09 Q3uOLS SI FWSAVI CSN01S JW SLTNSFY CALNTud (2N03xX3 SI TOW 3AvH *303X3 NIG ‘vO (311 dwOD SI T300H AVM *NALNO=1‘NIG=€ ‘SA TAMSN=I ‘SNL (4*0=T'SITAM3N=T | S00 1= I ‘1 WN=d) dvd (O=1'4 ‘G1 W3NEN YS=1) SLVOdN * dad KON=83dV 1 ‘139 * Led yONd=Z3d¥ 1 ‘139 “ddA ONd=130dN ‘138 *ZBOUSI=NN/ JAGMdIU=US ‘139 3OuvHI/ uasn/ “OOOLLEHI'O00TL Ed 'd0L gor / GS0NTONI RW SNOLLWITSICOW (GNIVLGO AMLSWAHLVE (MOTE se3LONe* 335) GSNI¥LaO YL¥d (ANIV1G0 SNOILY3I4100H G3NI¥L80 SI T300H SAvH (314193d5 SLIWI1 30undS3y G2 Goexond 103/ COKKSEKEHEERRETTES ERE KEeESETEReTecEreresereeeaeeeeRaseeseoesEgees NBO) * INSHROD “COZU3GAD SHL NO LSIX3 LON S300 <1dl0d0y =“ LNSRHOD * INSMHOD (93d01 LINN JOIAS] WO1907) “NY TOGH SAYA * INSAROD FHL 30 SIWISIY FHL ONINIVINGD 3714 INdINO sLNUdddY = LNSHROD * INFOS “SINSA3 NOILIDSX3 8Of 30 AMVIG YO TITSAVO = 4AN0d0N =“ LNG) * INGO “(3A0H3Y 39 1ST ONY CSYINO3Y * INSAOD LON SI F115 AMLSHAHLYE 3HL S3553000 HOTHA NIT * INSMOD WOE SHL‘AUWIOIWXS NI O¥3Y LON ONY S114 SivddN FKL * INSHOD NI 3000 NVULYOS HLIM CSLYYSNI9 SI AMLSWAHIVE SHi 4] *#Jt0Ne* = ©“LNGRWOD (B3dvL SOIASO LINN W1907) * INSENOD AMLSWAHLYG SNINIVINGD JTId vied = oO co Feed (MULTIPLIED BY 54 57 60 64 61 63 45 49 64 66 48 73 67 68 70 74 G7 10.) 86 82 76 86 82 74 870) 82) 73 88 85 78 RCPPRNT RZSVSVFRUFARHLSSsssetees SeEURFeR SE a= 67 (Sheet 1 = 20.000 60 0 0 0 a) LL LY O10 00 0 0 OO) (0)0) 20) 70 OP Aa) a OU OM Orn OMe TOUmO nO eri Oey Oe Oy OOO ORTON OR OR Omni Ole OM Oke Onn OmmONin ORO! mOnstOC ROO! OT ORT cOR 0 On AON NOM ION ON ON Os On Onn Ont Onn Onis Ole Ol OKO Wi0! arOss0 6.0100 RO) OO 0 OOOH ON ON On Oni Oli Ohne Olan 0 O 1 11 One0; Fy 0 0 LLL Gal Lie eit ie tt OSL My Leet Lee ll le a end 2.000 PERIGD= 12.000 ULL e lt it ell eit) a a On Om OlhOhes0: 120 OO OO OPO OVOe OO OO Oe i’ OFF Oa O00 0000000000 00 0 0 ORS) OF OF Oe OO: m0) 210) 720 0) OO ne0 HEIGHT= 1.) 0 ON OO Om NOs OO) sOin Os On Ol Olen OnuO! a0 0 0 0 0 ORO MON MOM On On Oni Ori Ole Onin Oln 0 0 0 O if i1 22 Mf (ULTIPLIED BY 1 ORO) WORE TOLL eee LE TLS OL ea ee eta et 0 0 O if ih 11 if 2 fh Mf 12 42 12 12 Op LON MOUNT Lelie Tie eel te Le 0 0 O fh 12 Mf Af 12 12 M2 af af 12 it eT UL et Ul SUL OU bt ht ERE bye by oul 0 0 O fll 0 0 0 fl! INDEX 14415 14 17 6B MOAN2BwAHBAH7BAAHAUARNRMBHAHR HTD B LT et ele eh el ee ant OFON LOOK On (Ol OO), (0M One Ol) Orn .O)sis Ot 0 ain 060) e20) N10) OF SOS NO a OnnKO ORO TOON OY LON ON “Om Ok Ol On O08 70) O)G 01550) 1x0! 250) 0) 0) 80 20 2080 LR ie Lee Ly LLnL elt L OO On ONO OO On iO eT Mt Tt 8 LLL LL TS LES DL bel 1 elt tL ret ot et St ihn EU ADV SEY RE ET SU Ey Sele tes OU bbb ESSE he hE by SEL KE Tuy hy sey oul EE EBV UEC aR Wb Tu SOM abla yheen bles bis bys Ghee ht 11 if if ii ii ff 41 a1 if OOOO Ones Ol Om On sO OMn Oi Os. Ol 8 (One Olin O ss Ouer 0/750) 710 41 al if BREAKER IJ: 3: 6: 7: 8: as 10 : ll: 12: 18: 19 5 20 21 THE DEEP WATER WAVE PARAMETERS FOR CASE 1 ARE WAVE CONDITION oo oo 0770! 507 10 ONO OM Ol MOM Olu One On Oles Ola OjeO) m0) iO) 0) Ole. 0! a0 0 0 oo 0 0 IO Oy 0 0 On Om Oe MO Ol mOn Om tO nO On OO mMOM NOM NOM Oc 0s 1OunONsi0l SOR m0 suOsmaOlna0) OPO MO ON Onm Orn Onn OOH MOO Ona O)nn0, On Ons Omen OignO! Or OTE Ol On On 0 Osh) 20h 0 Ol One Omen Olan Olt Ota Ole Ont Orem Ol an Ol anOhel0) sn Oleg OO) os Onn 0. ON OW Onn On Ola OMOl Ol Om uOl i Oj nO) mx0) 10) GlO lO 2 Ol7n 0) st Olan Osan0, OOM Os Oe One Os OR Onn Ose OlmnO, Olen OinrO) NO) KOLO) 710) HOO 0 000 0 0 0 OKO NOM HOM OM OK a OM Orn: Ooi O ve Or lO Mm OniO KO. 0006000 0 0 0 0 0 0000000 00000080+08O 00000 0 0 0 O08 Ore OR ORONO On mOn ORM OM On MOM Om OlMnOnmOn 0) 0)t On kO sO nuOlin 0 0oo0000000000+0O 0 00 0080 One ON Ole OO Nn Oat On Olnt Otees Olin Oren O)n 0/2 Olmn Oem Ol One 70/110 0 OF £0) Oy ON OF On OM 10K: Ola Onta, ON ONO ONO) GO AAO) On nO) 50) Oi 50 0°10), 0)" 10). 10 QHRARSRRRBSZARBBBBRBRSSSSSTS 0 0 0 OOK 0) 10 ONO O80) 510) 00) on0) 940, (Sheet 2 of 9) ONO ON 0; OK On, 0 OVO F = OO ONO Ol On 0 G8 Figure G8. 0 0 OOM OO TOMO Ona.) Ona 0 0 0 0 0 0 0 0 0 1.) (MULTIPLIED BY (DEG) WAVE ANGLES 27 928 29 930) V3) 132733 34 35 436) 97 928 26 29 2g 724 Eo 2e 21 20 7 eG lg 14 15 16 VJ: Bil OM OTe res SHS OM Git Onl ae Fikes Oe Anis OMe eee ones TAZ Ra a lO 2 1 7 UU os) YG) Sy rf Ey 5 7 u3 10 11 Sie Sale Ce Spey G) S896 Gay ae, 13 14 8 13 14 Sis 1! i314 Iie i415 DZ eat ely: eli, ma G yates eats aml BamelOlspl2 GW ne 7 1 OSE, 15 i5 14 il & 5 OS tS tS ee 17 16 16 14 11 1} 16 i7 18 19 20 -, < Ch es A em OS age ie Oger a7, 4-1 -3 -4 -5 8 8 8 9 9 9 9 9 13 14 4 2 0 9 1S ales rel Sel Zoho 10 LAS al NT a OT als ws tO 1 le 4a 10 12 af ey GR AS A 2 oy ey ey 1 =e ~4 “4 -1 -6 = 480953 7 14 16 16 1G wale) iS 0 -4 -6 -6 4 LS bs) eG) SG i Pa, Si 2 li 12 Fe Ol Oat LOG iloiy te 14° 15 Gy aky oa) ra 14 lo ae lS ele 7 2S a OO ee OMT, 13 ale 5 1S i314 10 li 10 LO ORAZ ae 145k 10 10 10 24 5 4 < 0 1 14 13 By) Ue Ri aL SR) “3 c re) 10 10 -3 -4 Dag 3 LORS lO Helles Des ml One 10 11 Sah, Se al (ye) U 6 q 9 Hah 72174208 12 al ee 12 11 li 9 10 i HA ye ul 29 (hr dhe, 10 10 LO LO M0) i? faNS LO PO eb att 9 a 9 10 14 i3 11 10 4 4 FetO) LO eA) Hit a 9 eft Re vay} a 13 13 32 = Ost 9 Lalit 9 Fe TAG a, ee 9 9 144 12 10 10 14 fete is, 12 35 36 37 38 9 40 4i yi GT Wi ee Hho $8 10 10 10 19 10 10 10 11 M1 11 fee teh ta) Pe Bi Bae eee ht] 13 14 14 12 14 14 12 13 6 9 9 12.14 «14 12 i 1S ial Sal 2a tel ZN Sola heel tl 13 9 Baad 8 Tae O hen 8 en Oe BS a 8 tea 8, 9 Lael eels yl 2 1 42 5) Be PRG eRe ee ae EGE ty ty 10 re 37g a ST a 44 (Sheet 3 of 9) Figure G8. G9 WAVE HEIGHTS (MULTIPLIED BY 16.) WS 14 WS) AG NB 1G) 20) 2A Zee 2aN 24 2a) 2G 27.) 28) 929) 80) SL SZ uso S4 soy ones, 1 TE RD TO Te net RE ek ele ed ee Sn ta eT a Nei. Rela mele Gs, Gilmer te deed 2 BAI PACA MN en AeA 9 Ura el TR te La aie Kau Gace Mia La > Uae a SSA Sak SU te SU Shs BI 3 oT) abet) Wer 9 ley Se 9 ma Se SLM a Le STs ae et Le GSU We Rae Hone SO EE SG A Fe 9) 4 pee ct att) Gala 2 Nap i ot ne Gly hart Eanes ch ry 9 beth cs Some AV UNRE eae ape Folie SFM bE) ASV GUGS Can Granites vf a See eh el MAG Rel Remi ed colt mete Ul eeu Gyn Meee 7eem 6 BSB MOO NG ae a ne eel tue ere tee Ret Rls Ges i Gr wey, aie Ol O) Onan, 7 NO Te 7 ao ee nO hon ee SMe ikG mmo n TA Mh7e iG) am? imo at Onna Ohmi 8 OR STE ETS BP Ah tay oe ty TT A SPS Sy apes sle2 9 OE SE ET Pe ef ah a a ar} © GY GP SI SU Se sae Shey 31g 10 HEN GP GER a a ER SS) a Se Sy Sk VS, Ty il Lea NaS Ze OO Se Pea Bie BN MBF lO aie Se elo Gol G16) mlz 12 17 LIS ae et 7 MG lone Simul 2 it Onn O Oman ot 2melsinl se eliza20nzZ20 22) ele e2lu20 13 CEH LT VeiecOl eco 2442S Oe toa Slot Gl Gi20) 21e9 SON 50) S029 Mrz see T, 14 ZO We 120) eby ON 2al esp eles ee ee eee Te ZON et i2A eZ bnnzG 29) he) 929) ZOO 15 2b) Zon P2OWN2b e2oe 24 e238) ZN O21 e221 20a Dlno2 au eon hie ZB) 12028 27, 278 e2ON o25 16 ZaieZon 2orZoZ4s e243) 924 520) 2020) 19) 19201 22 24 2b) 278 2B 27) 27 2b Zak 17 ZAR AN 2A 2A 28) 22 2 20) 2009 9) IBN S19 2 2a" 2b) 27) 27) 27, e2Gn 2a 2d 18 25) PES 2a 2a eA 2s) reaiewe ly 20 eo, O19. 18) 18 M92 21) 923) 25) 927, 27 eae) eee eo) ee 19 POs LSI 25 esi 25) 2s) 22) JONG MB NB) 1B) 19) 321025) 250 27.) 27 2b) 2a) eeoa| 4 20 2S 2o 2a neese eae P2828) 22, 2l) NOP BB B89 21 2025) 26) 927, SZb) 2G) oe 2a24 Zi SanZaned e424 e250 28) 2521 NOME OE NB els 21) 23, 125) p26 270126) 2 eons 22 2a eons met 249 2A: 925) 123 2120/19) 1B) IB 19 20h 2350 ae pzhy (27 zby 2a Zayrcaeza 23 2 Pea) 2S yes) ZR 24 2423) 9722)0h20) 019) 1B 1B 19s 20 N92), 2b) 2b Zoyeebe 230 620) zoe 24 Oey eames 24) 241 92828) e227 21 9 AB 1819) 205 250 Zhu Zo 26) 256 -Zolzon2d 28 25 LS 2S) V2a 2S) 25) 2424) 25) 922) 24, 20) 9 IB WG 21285 26) 26) 26) 25) 258 24 282k 26 25) 23) 2323) B23) 24) 24) 238) 622 21 20) AF IB 192 1'e 23 n 2b5 126) (26) 25, (25) 924) 428 27 2S eS e2en 23) 725) 24 24) 28) 28) 22120) 19 OG A922 9230 25N 26) 2a) 2a) 24) 24) 242k 28 28) 923) 227022) 25) 24 24) 925 23) 922 21 9 19 20) 22) 24 250 26) 25) 24) 24 24 24 24 29 2S N28) 22 22 23028) 2325) 25) 22 vet S209 20 22m 24) ZN Za) ZoN Zay 2424 Atk 30 ZS 2a) 2222 923) 282825) 925) #22) 21020) ONG 20 22 2A 2am Zoho Zane a) 2a ea Zk 31 25) 23) 220 22-2225) 2325 125) 22" 921) 920) 119,920.22 238 Pozo) 24) 24) 24 23; 923) 23 32 23) 2522) 22 220223) 23) 2325) 22) 21 20 192022 230 25) 25) 24h 24! (230231925) 928 33 ZE2S 22722 N22 N22 2223) 22 2221) 420 20/9 20 220 23" 24) 247 2aY 23, 23 923023) 25 34 29) 2322) el) 220022) 922.22) 22) 22) 21 20) 20.20) 22123) 24) ZA 24) 23) (23) 23) 23) 23 3S ZO 25 O22 eA 22 ee, ee DIU e ee 2h e201 ZO ZO 22 yea urea Zanes Les 282s 25025 36 23M ap ree ZW ea Ae ee ee eerie a Wee) 20M elume Perea. 24) WPAN ZON 2)) 250 Ses meeS 37 Zeer 2A ANG ee) 220 22N 22) 21) P20 20) 20) ee zea AEA) ves 25m one SEN eS 38 Done 22y eel eZee el eee 22a eel e2 120) 20) e202 22a a) es 2S 2S eS seZ ous 39 Pas FEB Ha PNP VPA PAU Aa AN ASN PAY AR AD onerQ) 0 Zama AD ABI ARS VARA Fe Fa ARS O2RS AR! 40 C5 22) 22 ZA AA AAG e221 AZO 20) 21 22 22 eau 2a 2s eee 22 22023023 41 Revved waele 21 er AL ieluety nz lu ei 20) 20 21 eeueee 2am es eeu eee eu Zener eee. 42 CPRESEIEN PRIN PSMNIPAY AN PAUL ZAL al. PAN Za PSU PANN ed Vilar PMS PIP ed! PD eae) eae) 7d 7) 43 CHE IPR A CON PAL PAU AA ik, ZAU PALL) Zale PRU PAN PER PR) RSS A) Fe) NPL PaO) PP) 44 22522) 2 2h) rae 21 el P20 eee 2121 et 20 20nd eee eeu ee ee ee 22. 22D an ee: 45 2222, 21 2d) 21 2A eet 2 2 21 21) 2820020 eel ee rere Oe 2282222) 222222. Figure G8. (Sheet 4 of 9) G10 23 BBBBBBRBBRABR WAVE NUMBER (MULTIPLIED BY 1000.) WTe lS ilo) o17 VAR) e19 (20) 621 422 923240025 626 427 28927) 980) 31 V32 53) yS4 155 36) 537 | 3B 1 5 303 303 303 303 300 303 303 303 303 303 303 303 303 303 303 303 303 303 303 303 303 303 303 303 303 2 : 303 303 363 303 300 303 303 303 303 303 303 303 303 OI 303 303 303 303 WI 303 303 303 303 303 303 3: 3OF 303 303 BOF 245 JOT IOI 303 WZ 303 303 30F 303 WI 303 303 403 303 WI 303 303 403 303 3 303 4 : 303 303 303 303 303 303 303 303 303 303 303 303 303 WI 303 303 303 303 303 303 303 303 303 253 275 5 : 303 303 303 303 303 303 303 303 303 303 303 3035 303 303 303 WI JOG JOT 182 176 148 156 144 139 142, & + 142 146 163 145 205 230 303 303 303 303 303 303 303 W3 303 303 172 170 134 134 127 122 122 116 120 7 : 114 116 121 114 132 122 150 156 184 210 240 235 207 213 182 148 134 198 127 125 121 119 114 116 111 8 : 108 109 112 141 119 115 127 123 137 139 144 146 140 137 132 138 135 128 118 116 114 113 107 103 105 9 + 108 109 145 121 120 127 125 130 129 132 133 134 133 131 133 128 126 121 112 110 107 105 102 100 100 10 : 110 112 114 119 120 128 123 122 126 131 130 130 128 128 125 124 120 116 108 107 103 101 98 96 97 11: 108 109 112 114 117 120 120 120 124 128 12B 127 124 124 125 121 118 113 108 105 101 100 96 93 95 2 + 104 105 108 109 111 114 114 120 119 125 125 124 122 122 122 117 116 110 102 101 100 99 9% 94 % 13: 100 100 101 102 103 103 106 109 112 116 117 118 116 115 113 110 107 103 97 96 96 96 94 9B 94 14: 93 93 93 94 93 94 95 99 101 106 107 108 107 104 106 101 101 96 91 91 90 90 WH 91 7 i5 : 89 89 86 89 88 87 87 8B 91 97 98 98 9% 94 98 95 93 9 86 85 B84 B4 84 83 84 16 : 84 85 84 984 83 83 81 78 83 89 91 91 88 90 91 88 8 B4 Bl B81 B81 Bi BL 80 80 ines) 82).82 81.8078 .78 <7 .76 79 85 86 85 82 84 86 83 81 80 77 79 79 79 78 78 78 LOM o IWS ld a78 376 78) 7% 675) 9718 AB 680 BY 27 479 80079 A718 BT ald B97 B 7B 278 LOM NOM G eel AIO HIS a2 WIS WAS p74 ATG BIG AIO vl AE ll WTO O REO BIT wall uid BO 679 nT? a7 8, ZO MRT To yiT tl JS f4 TR TA 7374 TS 73 oS TA 4 T4374 OTS 077 2.78 80 (80 280.80). 79 PA os Oe 50 79 6 74 78 TA TS A722 2 ATA TA 7S SE) ATS 8 Pm OS OSH Roe wal aATC a7) Alb) Ho) aS TA OTA ATL 70) nf Ohi nae ad amT Outta POM IES Os 88) AOU GAO BAT io) wi Ak All WePh) G9) n7 069) 76790176) 480 24 : 84 84 84 34 82 80 78 74 74 72 71 70 69 69 6B 7i 76 76 79 Pot hes wo 84. edd 82-462 79 78 76) 7S a7 270 469 wf 070 TL 277 TT 279 979 980) 80 80\.81 al 2OMN OS on ei 8S) AAS 82 8079) 77 Vt 2) 70 270) SOF Tl edz ant ed 078) a7 B79), 979-180) | BO). BO Piso? GS 8S GE? OS Bl 9 lb ial4 ale tk KOD SF eI ae WAO eTOlugl fiat) aIO ag 0d 19 calle COMBO MONS? USP Bee h2 EOI NT Vito aS MOSEbT wil S un 4 eld 70 wl 8 WB oa7B\ ahd arg PONS ABO Bl eS VBL AG? 80 li 1D). a0 OB 69 G10 WIZ iT IuM a) TO ATO sal «G27 yal B)g18 978 SOs a7G 79) 080 80 80 >80..79 pne7b 74 72 7068 48 972 71 TA Th TS T9916 Ib TT 777 Sluice), 978 8 TB ATS O18 AIT iTS TS oA 69 67 LOT VOB X70 TS) ATS 4. p70) WD 970076 976.076 PRM NATO MAA WTO MIT AIG ATOR 4 a ual OWO9 BT OD ATO Oe GT Suhh®, GIA TOTS NID Nl O\.010 TSM OID AIS iD e7 SAIS ATTA RTS MT oiONUOT WOO OT) OF MIO nT SUNT S IGT a ngs NTA BA NS TA ATS ATS IO AAA TS Ate GIA OOF OT MG MOD KOO MOO ATO IN2 TSO TS, ga AA GTA 73 72 SSSR 2 eI BS 2 SMTA Taro) PEW OTA AeA Z nL Wel NFO WMGRUNOT MOT Gd OF NOP geOT UWE WRIR Mie Lae BOWES MMIC e wel rl ATO vel OP MOF (OO) N67 Ob pGR (GS 664 G65 GOOF) eft 972 72 B7 fiz 2 70 69.69 69 68 47 166 66 65 64 62.64 (67 67 .70 70 71.71 72 72 72 72 72 Aes wat) A706S KOT NOT 67 GT Gh Gh WiGe 164063 62 064 Wi67 067 4G? 70 irl wil etl at atl) a7 ti u7A 39: 70 69 67 67 66 66 65 45 64 43 63 62 62 63 44 65 49 69 70 70 TL 71 71 71 «70 40 : 70 69 47 4&6 65 44 44 63 63 62 62 41 60 42 65 45 48 68 479 67 70 70 70 70 70 41 : 69 68 46 45 64 63 42 62 462 61 61 61 59 61 65 64 68 68 48 42 : 68 48 45 64 43 62 62 41 61 41 41 40 59 60 42 64 47 67 68 43: 6B 47 65 53 62 62 6! 41 41 61 460 40 G1 O61 44 64 47 67 44 : 47 45 64 63 62 40 O1 dt 41 40 60 40 41 G3 45 64 66 66 47 5 : 6b 66 44 63 62 St 61 61 41 41 41 40 60 O1 42 63 65 66 Figure G8. (Sheet 5 of 9) G11 2 WAVE CONDITION 1.500 PERIOD= 8.000 ANGLE= -35.000 HEIGHT THE DEEP WATER WAVE PARAHETERS FOR CASE 2 ARE: 1.) (MULTIPLIED BY INDEX BREAKER 14415 1617 BIIDAIANDBDABH7BANHWNWMBAHH I B WJ: 00 90 0 OO Om AO CH Oy AO Oe Daye Mey Meee ee TS lan ib bie ttt oD bb 1 OU et OCMC MOM Om OM Mei My ell0 ttle Lode och) eM til ioe ellen eee OOM OMMON CO Memliuitt melt) tt elt lieetl tell cel teot tacit cmlt gos le keener hee lemme SEU CU ie EY TRL TET Uh UY LE SU SUEY el SU fags eed US Seba B oR AV bed ht 30 1 SD TY AW aa el EVM Ge SET RU DU Uy SGU Dane Slee Seah aah t One Cin OlmO mm On titel 5 = Oo -_= = Oo -_ = Oo _ =_— > _ oo oo oc = Oo _ _— OS -_ “ “ «4 =“ “a _ ~“ = =“ “_ _ ~~ = = -_ -_ —_ = = _ So O if 11 21 21 Of O if i a1 a il O if t1 42 Mf ft OO hel 0 0 0 0 0 11 6 7 8 9 10 il 12 13 14 15 16 17 18 OO nO Oa On Ou Olg0 OA Or BO sO ee Or 2 Oi rr eit O 11 11 a1 a1 Mt Oey Si ett 0 11 11 if a1 11 Ci AOMO OCiQie sO 0 0 0 O05 O70 iO OV GvOw GO Oo OO AO OVO Oi OVO ROO Oy Or Ove Ove Wine® OO vO OG Oe O —@ QO MAO Oe Qoe® vO i OO OO Oy On Or Oe OS Ore Wie Oy Orn & Ol Onn O mm O nm Ouan Olan Ot ONO) 0 0lnn0 OF Oi QueQ i Ol Oen OM m0! 0% 04 Or mON 01702705 01> 0). Of On Ol 10) a0 Ol. 0): Oma ain Ola, OOM OmmOn On 0720.0 (0 20h 0. OMen0. Ol 0" 70.07 0) 020 Ome Oc Ou Ole Onin ORG 0 OO OOO Oey Oe Qo GO OY OMT ONmOmOumOn Or OnnOn On 7Ocn0n 10) (011 10 100 10Ln 0 Onn Ooh Oma 0 OOM TOON Ol OmnOn Om ON 10270070 OM O Onan On Or Ona Oe Ol 201s Ont 0. 7.0m Oh 0 00m Ole Onc una. OO OmrOn On On O17 O00. 0 P70) Or TO ne 0 0 0 O20) 0rr0 10) 10a Ol 0 nO O20 ean Osan Ona O. OO) er Ohne Ol nO: Ot Cana Osa, HOO Oia Dy Dire Oi Or, & OP 00 10900) 470) en Ohn On Onan Olan Og Oneal Olea, O O70 0105 0700.) On 10) 10 0 OO) 0s Ones Oe Ome C aC OO Ome On 0 0 0 0 OnOL 0 oo oo 0 Onn: OMmOnemOn nO, 26 00 0 0 OO Ce0 ORO; Om Ok Om Olu Omen 0, 0 0 One On Onn10) OF Nom Ore.0 0 Omron Om On OlwOvn Oy 10m O. 007 0 100 Or Ol 0 0 OO Oun Onn Ol Om OnaO OOM OumO MOM On OnOUr Onn Orr On nO) 01 On 200. OL nO Get 0 0110) fa Oa Ole OMmLO. ONTO OmOnmON Oi On Ont O'n0% 710) 10.70 Ol Ol 0) COO sO 10a Om Ola OmmmO OM OmmOM NON On OM Om ONn OOo 020) 0. (0 muOL 0 ooooocococeo ooooococoococlc“(s oooocoocheca“(s oococoooocoo oooo coco occ oe ocooooce ce co ooocoocoococe ooococooococoeo coococoococmcS ooocoocoscoeo ocoococoococ;a coo ooooceo ooocoooco oc eo oocoocococoeo ooco coco ceo ooococeoocco oooooceoceoe ooocoocoococe cocococeooocoo ooooocococococoeo ooocoocoeoococeo eoccocococece eooococococoo eocoecocococoococoe ooeoecoocooceo OMOM On OnmOumOn On tO) OOo Oe On 0 mas On Onur Onn Onmt nme Cie OadO OO MOy OM OL On On On wOne On 0) 70.11) ON TON TO) On a0 Al ONO Ol On Om Oca Ol. 42 Or On ON ROn OmmOn iO (On mOn Ons Oe lOO. Ol sOn Onn OtmOii Ou Ou Orin Oa Om Osmo. On Om ONO On uOr OmmOn ONO) 0 07 nO OnmOlan0 43: 44 45 On Om OL Ono O Onn, 0 0 0 © 7070) 0" O00 ONO Or mom OF NOnm Ont. tOnmC OO OH MON MON: 70 0 (Sheet 6 of 9) Figure G8. G12 WAVE ANGLES (BEG) (MULTIPLIED BY 1.) 1 Eh SY i) SE a ELS Vey) soyy ay ay RY PS HY eC) LE a) ede eR LY 1B OY ey Soa ea et) a) ay erty cay ef ted Sel aT af ty ch ah ere eee Rhee) ep} ST ROM ie OM oi Ie On ae On Ome SOM Zi Man Rom Ral ROM Fon) e OM 2a AMS en Ai Oh Be Oh SIP I teh ea et yf ea ety ay ee ea Sh ey Co hay CY yl ye eR th a Sit ec OM in ay Coen een Odeo Ate Un OM tana m Go mcd Omit lite CR tintin alee lane toy Se Ol si Ol cou ey oll lon ae mina ea Onl ON teen aa ls Vie als lon laa 14 LOS tM 2e oe oN A222 eo SO On lOt lula sala EB} AU UIE IS ABS AY aN a AKO) A LI IA ayy Ye ba IIe RR Ned HH a lay A/V Meal inl Onl ta LON SR in e107 oh coos i ei aOk ah lOi ana lOon- Lin lel Gali =12)-15' 18) -18) =18)-19-18 lone ten lShy Sey oy dln Ie a7 icon co ol Oyo LOR Selo 20n 19-20) 18 te) Hy Lally, iy) a Pal cra rat) Al) 1S OMe oa SBN Ti) Bh BIO On 7s baa onl Olea opal On 2I oe 2ee eat Lee Welle Soo sBhs Sie Te Bil Ori Sy oe oie tent on Sloe S ly 21 2an 24a 2a Ze 201g Lote lone ieee lO Be 7 7a Bille s7)) Bt) Olay Vaal 18) 200-23) 26) 26) 2oe 2a 22 N20 OMe Loa opi Ol SB 87 Sie Or 10 Bab) eta opal 2d) 2620) co 2c a 22) 20 Ue) 5 ANS ay I as ier pia Far) a) A) Ts) I HUY SO SPRY Silay Cras} RN) Par PT) PLE AR) C7 — Oo ao 1 i ~ 1 — > 1 a uo | mm oO 1 ~o 1 ~ I ~I 1 o 1 — o 1 so 4 ~ i} an 1 on 1 ~— U ao U ao t oO 1 oO os bo * ' — o i] — p ' — (FH t a8] 1 co { ~ 1 co 1 co 1 -o0 i oO J ~~ 1 on 1 o 1 co LOM aloe toh loe Iwo, | oa - 9) Oe Be BiB Biol t ob 2en2onn eo GO ole - 202724 eee 20 ie Chelona lia Or 10 hoe Bis Bei Bin Nin lor 19 een 2 7k sO a-Si SI Zon POU on ee 20 BM) 8 AU A ANS) SMSO ic Ith P/N th EE ah ay aN) Pah Par) Seba | Par Po Yes) SPR) P| CoPA0) CA ona sl NOE 10 oO 77 6 85 9b 21 26) sO. Oly 80 Zea 2O) 24) 222 lO Lie Ae aoe te LOO 9) Bie 7 OOM rm le 220-2) a0 ol 200 2] 2Ou- 24) 220-20 he Salome te eum let oON —9 ae Bin CBie Bl 9 10e is) Ne 2s) 20 On OO eed eo 2) eo een 2019) Coe oe ton i109 98 (Be 8) 910 18-18) 24029 291-29 0-27 -2o 22a ele 201, Claas Se Pee ate T1109 9 990 910119) 24 12820028 27-2624) 25) 212019) C2), BD Ve AS I HES SO AS ee) EUS CN bo Pat) coe hs) Pas) V4) IY) Vay IPS bP IN AIAN) DY) Cea ae Sec iehe She Sie ie OORT Or 1O Nila 2 2an 27 2a 2a el ea eden 21 1G 18 Pas) SUS ay SS SS Nh HU esl eh SU Ua Weel ay PA ie Ney Pas Pa sf Pay sa) PRY Yaa PSL CH) 29 SPS ENS YS DRAUSS ah Soy PD | Peay oP / Yas ITH) eas P RY Pa Saat) AN ah SOM len eee tse te tet heaheelo lane 22) 242 eo) en oye a 2a e i 20 lo 1B Salty a1s =1SSl81S15 -14 ay I-23 26-28 Ze 2 eon 24 eee —20 la ily Zune PIV Se Saha PS 14) N44 Kop 1o) S18 2820) S20 20 mer 20 24 ree 2120-19) 19 Ch BAY IO SAR RS a Mh SE NCH aH ta} Cal Me) op) ee Sa YLe) Pas] PAs) SPT) Pala) PL EPO 38) ale a) Caneel 2 tata eto t6 P6167 19) 24 2b) 2B 2027) 20 2a ee 21) (20 1919 S18 S14 1416 HOt hi te 20k 25) 2a een 202i eh 2 220.20 19 hl, tees Salo lorie ee KIB 2 Pon 2 7) Zena coh zon 24 22 220.20) 19-19 Sale sea 4a tou Waal 18 19) 19 1222627 282020) eer cee ed 20) 201919 Oa a ley lsh AE Ten— 1718-19) 20" = 201-2022), 26) 2) ceo 2 in Zo) eo meen 2120 1-20 S20 017 Sasol a Talo te ie to 20h- 2th Pin 2 1) 2a 26 22h ein eau eon eer el 20-20) e020 AONE loa tao 1G) 118-200-212 22) 229-28) 27-221) 2b 24 2222120) 201-20) 20 Ohloh to ol 1B L221 22-22 Den 24-26) 2G) 20 eon ea eeu) 21) 20k 20t=20n 20 Loon lol—loy allo 20 2 i= 22 22h 2a A ea ZO e Ol ce eon concen elie el 2020) 2020 lon lon WS IBi 19) 21220-2282 On ee 24 col eo Zoran Zonal eli ela ZOE 2020 ER 20, Aa Ni lon a LBl 19) 20-21) 22-22) 230-2 a 25) 2426 -2al ea ee 2a ele eed) 222020 Ae Ob lean, =20= 21 220-25 e282 2S, cau Poker co canoe ae) wel ele 22h 21 eH 20 ° 1 rs > i] — Cal i eH . . ! _ > ' — ho ' roe ho > > [Rsk C= Figure G8. (Sheet 7 of 9) G13 WAVE HEIGHTS I/d: 14 18 ST eWnepe ay inte Zase Be it BiwiByy pasha dl Aue La aa hie uel hal (0G MOe 0) Pig ate) ahh Bike) LG) aah2 Geel Omnl'e, LO Msp att: ee LoL: 12 18 19 13 18 18 14 18 18 Nay BY 3 Wey ahi) sel Wa) Mees 18 16 16 Oh LONnLe 20 16 16 16 16 22a OuelG 23 16 16 Aas Onn G 25 16 15 26 16 15 27 16 15 Pas}eri my Ska) lis 29 {5 15 OMe! Selo 1 som ajelo Poe) 5 hey 23) CE IB la. Sane olay 14) 35 14 14 36 14 14 37, 14 14 38 i4 14 39 14 14 40 14 14 41 14 14 42 14 13 43 14 13 44 14 13 45 pS (MULTIPLIED BY Bl 22525) 24 10 13 el a ee LO ee SS I oe = Oe — a t i oil ood hmMm MN i Bh me he i oO 13 13 Figure G8. 10.) 13 —_ 13 14 a 14 — 14 14 (Sheet 8 of 9) G14 WAVE NUMBER I/d: me oD ONO Of PS OP ee cn & Ot he ee — Se oon oe Nh So h2 = 22 14 15 (MULTIPLIED BY 1000.) > 494 454 495 455 456 456 456 456 456 4546 436 456 456 456 456 454 456 456 456 456 456 456 456 454 454 > 454 494 455 455 456 456 456 454 456 456 456 456 456 456 456 454 456 456 456 456 456 456 456 454 456 > 404 405 415 415 456 456 456 454 456 456 454 456 454 456 456 456 456 456 456 456 456 456 456 456 456 > 456 456 496 456 456 456 456 456 456 456 456 456 456 456 456 456 456 456 456 456 456 456 456 380 414 > 45a 456 456 456 454 456 456 456 456 456 456 456 456 456 456 456 456 456 275 eet) 174 164 145 167 : 164 > 159 54 we > 143 137 129 « t25 + 120 120 sebee. — hs Cn ell call acelllll toeelll eel =) 224 177 14 144 170 146 160 153 144 137 130 124 12} eg} 122 126 128 129 129 {28 127 126 124 123 121 120 118 117 415 114 113 111 109 106 108 107 106 105 104 103 245 184 170 174 173 165 163 134 143 136 190 123 120 tis 120 123 126 128 129 128 128 127 124 124 i 122 126 i18 115 114 112 116 108 164 105 104 103 102 101 160 100 249 309 347 456 456 456 456 456 456 454 456 456 456 260 238 278 316 347 353 311 321 275 254 203 208 212 206 200 210 204 202 195 192 190 188 182 177 149 184 180 i73 165 155 144 137 130 123 119 117 119 122 126 128 129 12 128 127 126 123 120 118 115 113 {11 109 107 105 104 103 102 101 100 9 99 202 180 i83 {83 177 169 156 143 135 128 121 117 115 117 118 121 124 126 127 127 127 126 i25 123 val 1G 116 114 tii 109 107 105 OT 185 227 174 192 193 182 173 157 144 135 127 120 114 ilg 115 115 118 121 124 126 128 26 126 126 124 123 120 117 115 112 110 107 104 102 100 99 97 97 96 96 192 {69 187 182 173 1a! 186 197 186 182 182 167 150 134 120 116 115 113 112 116 116 1i7 118 120 122 122 122 122 120 119 ay) 115 i12 {11 108 106 104 161 99 97 96 96 96 96 208 195 192 188 181 149 134 138 127 122 118 AS M13 114 114 114 116 117 118 118 119 119 118 117 115 {13 111 109 106 104 103 100 98 97 97 96 96 96 210 218 221 199 201 203 198 194 189 176 162 148 136 129 120 116 113 il 110 ii 112 113 115 {15 116 116 415 114 1it 110 109 107 105 103 101 100 98 97 96 96 95 96 Figure 198 193 189 177 163 150 140 131 123 117 113 111 110 110 110 110 i12 113 113 1i3 112 i 109 108 107 105 104 102 100 99 97 96 96 93 bi) 96 197 192 186 179 164 150 1397 131 123 7, 113 iit 109 109 108 108 109 110 119 109 109 107 107 105 104 103 100 100 99 97 96 96 95 a) 95 93 G8. 202 194 189 184 177 162 145 i4 126 119 114 112 109 108 107 107 107 107 106 106 104 105 104 103 94 94 94 199 194 187 184 175 158 144 137 129 122 415 113 109 108 108 107 107 107 106 107 107 107 105 104 103 102 101 100 he) 96 5 189 i186 172 161 150 139 131 122 118 LS ig 112 107 106 109 110 102 99 100 101 98 (Sheet 9 G15 183 178 148 155 145 135 127 122 OY 115 113 112 {ii 111 111 112 112 112 111 ill 110 109 108 106 105 105 104 104 103 102 102 101 101 100 99 of 179 175 163 134 142 133 126 122 118 114 115 116 116 119 119 119 118 116 116 115 114 il3 112 110 110 108 109 108 107 107 106 105 105 103 102 9) 256 194 164 177 172 167 138 147 138 130 124 121 119 117 117 117 118 119 119 119 117 117 114 115 114 113 113 12 110 110 109 108 108 107 104 104 105 104 103 203 195 179 171, 185 164 156 149 140 132 126 122 119 119 120 122 122 123 122 121 120 119 118 117 116 115 114 113 112 11k iil 110 109 108 107 107 106 105 104 104 266 223 206 218 210 203 190 177 168 163 161 154 148 139 idl 125 121 119 119 121 122 123 123 123 122 121 120 118 117 114 115 114 114 113 112 111 Lil 110 109 108 107 106 105 104 104 192 1B 183 181 173 172 1635 163 157 155 155 152 152 151 148 147 138 138 129 129 124 124 121 121 120 121 122 122 123 124 124 125 124 125 125 126 124 125 123 124 122 123 121 12! 120 120 118 119 118 116 116 117 115 116 115 115 114 114 113 113 112 113 LILY 110 111 110 110 108 109 107 108 107 107 106 106 105 105 165 173 164 156 151 147 145 145 137 129 104 104 105 176 177 157 133 147 143 142 151 139 127 123 1 120 120 122 123 124 125 126 215 ie eh q APPENDIX H: SAMPLE FILES--HOMER SPIT, ALASKA, WAVE PROPAGATION EXAMPLE GQQUNOH “LH Sansty 103/ SEKRTCTTSATETEKOETLOKKSHEERESTTHREETERESHTEREKEREEESESEEEKEEEEEE LNSHWOD * LNSANOD “NOTLYWYOINI GOP GALy0aY ONY NOILYTIdwO3 * INBAOD WYYSONd SHL JO SNILSIT ¥ SNINIVINGD F114 LNdNO s1dl0d9Y =“ LNSWWOD “N30 (93d01 LINN 331A30 W180) “NY T300W SAVE “NSA 3H 30 SLWS3Y 3H) SNINTVINGD S114 LNdLNO <1NUddy “NSH * NSA “SINSAR NOTLNDSXS OL 40 AWVIG YO TITSAV s4ANGd9N =“ LNSHWOD * INS4W0D “CSAOKR 33 LS ONY Guinea “NSO LON SI 3113 AMLSHAHLYA 3H1 S35S3990 HOTHM 3NIT * IN3KOD TE SHL‘ATLIOD XS NI Ov3y LON ONY F114 SLvOdl 3HL “INBROD NI 3000 NVMLYOS HLIM CSLVYSN99 ST AMLSWAHLVG SH dT se3l0Ne* = *LNSHWOD (B3d¥i JOIA30 LINN W180) * 1NSWROO AMLSWAHLVE SNINIVINOD JIS LV = =d3dUHOH = *LNSWWOD * LNSANOD (43d0L SOIASC LINN W180) *1NSAROD *CSNS0ISNOD SOTLSTYSLIVuH * INSAND SAVE ONY AMLSWOF9 (IY SNIASIIIdS TU4 VIVO sLVOEHOH =“ LNSHWOD * INSROD “3000 JOuNds FHL * INSAWOD OL SNOTLVOTSIGON SNINTVINGD J1i3 SLV0dN Oo > > H9 WAVE HEIGHTS — owWON COOP Whe — — ee Whe 14 NwoOhPe PP PP HP HP LP LS LP LS A ot ee | 28 (MULTIPLIED BY 10.) 30 31 32 33 3 36 7 3B OF 40 41 42 «43 «44 45 46 47 «48 «49 «(50 S51 82 A eS aa a) Cwnrtytor fF PS PS LS on o oO oS fo Ff Figure H8. (Sheet 4 of 5) H10 78 78 77 74 38 —o1pP PP PP Pf Pf Lf _— SBIYYFYVSSYRYR Noe eee rene PRAGA eeAerAae soa SBSBSSSSVZSSPARSRRRKFKRVGSSLSSVASRASRVSSRRASHe anne ener onwn oO wD BBSh S S BARARASAARRRSRBSsSRAaasse HSUYISS®SLRRLSKKRRSSRRSKLSSLAASFGFABRS cusp nen neon ~ > SPP PPP LP PL LP BRERBSSLLSBGCRARGFRBZFSEBSHYVSAi ee ene neenne 81 WAVE NUMBER (MULTIPLIED BY 1000.) l/i: 28 29 3 32 2M BD 3% WT WW 40 41 42 43 44 4 46 47 48 49 HO 1 82 12oue 82) 58:47 42 39 39 40 41 41 38 37 37 37 37 37 38 4 44 47 30 51 0 34 30 Zeenaiees) sho 4 St 29 2Be29N30 29) 2B 2B zr 129929, > — > 7 & od ho ho oO ined co cB ined o hm a bh co 3 8 Ps hho o bo oO 26 26 26 iN oa RO o mo o to on Re HN BB on J an g EEGRHHRHAHFUVSESRSSSSY ha ho Po on KO oh, fa ho > 23 24 24 24 [em ho od pee) ho > ho > BS ho BRR REPEL RAERLS SAAR D f hm bo ot Nm tae] th tl Bb} ho fa ct : B Nm ho oJ cA s Bi BS DOF DE DE DL LEBEN . NM on hm 9 ha es ho = ho ty ho C4 Bes 5 perahed Ww > ho i nh ho hr ro ho ty bo Nm Loe ho ho fo ti tO ty ho ol mom Gi fo ho ty to Gi ho > nm rors [em fo com) bh Gl ho tee) hr B= ho os ho ca SS8SSrrp eae hs ho _ BRREBRR bo eS Figure H8. (Sheet 5 of 5) H11 APPENDIX I: INTPRCP PROGRAM LISTING ooeos sees PotD sCOMDECK PARAM C PARAMETER (1Q=95, JQ=95) PARAMETER (182=95, JQ2=95) PARAMETER (KQ=18% JQ) C sDECK HAIN PROGRAM GRID(TAPE1=TAPE1, TAPE2=TAPE2, TAPEI=TAPES, TAPE4=TAPE4, LTAPEG=TAPE6, TAPE7=TAPE7) sCALL PARAM Ceeeesececceeercesscescecessenceceeeretececcesteeceecessces C C DOCUMENTATION C Coeeseeeaegeserrensessenssgaseseeesesesneseteses sees seness C C THIS PROGRAM PROVIDES A METHOD FOR INTERPOLATING BATHYMETRY C FROM ONE GRID TO ANOTHER. THE NEW GRID ORIGIN CAN BE C TRANSLATED AND/OR ROTATED RELATIVE TO THE OLD GRID ORIGIN C CeoscesereereeceesecreceeeereeeesereoeeetererereeseseeEeTEe C C INPUT DATA (TAPE7) C Cesescegegeeeresageccecrccseacegeserseseeeseceeeeseeeeeeesse C op] READ (7,500) HN» M2.N2,ANG, XSHIFT, YSHIFT FORMAT (415, 3F 10.5) $ M= NUMBER OF GRID CELLS IN THE X-DIRECTION ON THE OLD GRID N= NUMBER OF GRID CELLS IN THE Y-DIRECTION ON THE OLD GRID M2= NUMBER OF GRID CELLS IN THE X-DIRECTION ON THE NEW GRID N2= NUMBER OF GRID CELLS IN THE Y-DIRECTION ON THE NEW GRID ANG=THE ANGLE OF ROTATION MEASURED FROA THE OLD GRID TO THE NEW GRID +COUNTER-CLOCK WISE -CLOCKWISE XSHIFT=THE X OFFSET FROM THE OLD GRID TO THE NEW GRID + NEW GRID ORIGIN IS BELOW THE OLD ORIGIN - NEW GRID ORIGIN IS ABOVE THE OLD ORIGIN YSHIFT=THE Y OFFSET FORM THE OLD GRID TO THE NEW GRID + NEW GRID ORIGIN 1S TO THE RIGHT OF THE OLD ORIGIN - NEW GRID ORIGIN IS TO THE LEFT OF THE OLD ORIGIN sees READ(7,505) GRDTYP1,GRDTYP2 505 FORMAT (215) GRDTYP1=0LD GRID TYPE 0 = CONSTANT SIZED, RECTILINEAR ANINIONININANANANANANYNNONIANYNYANNAANMDNNYMNONAAIAGIHA T2 Onrororwnre For WN 32 EaSZFSESSYF HEH = VARTABLY SIZED, RECTILINEAR GROTYP2=NEW GRID TYPE C C C C 0 = CONSTANT SIZED, RECTILINEAR C 1 = VARIABLY SIZED, RECTILINEAR C Cease C C IF: GRDTYP1=0 THEN: Cc C READ (7,501) DX,DY C S01 FORMAT (2F 10.5) C Coens C C IF: GRDTYP2=0 THEN: C C READ(7,501) DX2,DY2 C S01 FORMAT (2F 10.5) C Ceeee C Cc IF: GRDTYP1=0 & GRDTYP2=0 THEN: C C READ(7,501) DX,DY C READ(7,501) DX2,DY2 C 501 FORMAT (2F10.5) C C DX=CELL LENGTH IN THE X DIRECTION (OLD GRID) IN MAP INCHES OR CH C DY=CELL LENGTH IN THE Y DIRECTION (OLD GRID) IN MAP INCHES OR CH C DX2=CELL LENGTH IN THE X DIRECTION (NEW GRID) IN MAP INCHES OR CH Cc DY2=CELL LENGTH IN THE Y DIRECTION (NEW GRID) IN MAP INCHES OR CH C ATTETT Tie tittitiittititetiits tite i irri ti itetiitiisi itis C C INPUT DATA (TAPES) C -OLD GRID- Cc TITS TIT Ti titers tri t tsetse tt ititititrtir rier tier ere C C esNOTEse C ONLY USE TAPES IF GRDTYP1=1 C COMER SREROAHETSSHERORAEATES ARS KETHETASEHTTSHERE STE RES ETORTS IF GRDTYP1=1 THEN: READ (3,31, END=999) STR»NST,NEND,AI,B1,C1 STR=X OR Y STRETCHING DIRECTION NST=STARTING CELL NUMBER FOR THE REGION NEND-NST=NUMBER OF CELLS IN THE REGION A1,Bi,C1=STRETCHING COEFFICIENTS FOR THE REGION ooonrnaninniwnnn 13 MAIN MAIN MAIN MAIN MAIN MAIN MAIN RAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN SBGEFARSARSAESSSIRFHLASE SSS C C 31 FORMAT(AL, 7X, 218, 3616.11) C CRMREKSSRSHTEREKESESKESEEKEKEEECEREDT SRT ESERESESEREE STEER EE C C INPUT DATA (TAPE4) C -NEW GRID- C COOGERGEEETORTETTNGTEDNGDSONTNED EST GETR SDDS TFSSS 9999S OTE SS C C soNOTEse C ONLY USE TAPE4 IF GRDTYP2=1 C CeSeegaageeeKee see ESE HTS SSSS KE SLSCSESSSSTLESRESSSS HS ESASSSES C IF GRDTYP2=1 THEN: READ (4,31,END=778) STR»NST,NEND,A1,B1,Ci C C C C STR=X OR Y STRETCHING DIRECTION C NST=STARTING CELL NUMBER FOR THE REGION C NEND-NST=NUMBER OF CELLS IN THE REGION C Al,B1,C1=STRETCHING COEFFICIENTS FOR THE REGION C C C C C Cc 31 FORMAT {AL, 7X, 218, 3616. 11) CHCKHKHLH KAAS SHAS SKK HSE HSH RHSSTESS SLES ER ESE SERRE C C INPUT DATA (TAPE1) C C SAGCHRHRAHHORESS ASS LSVSHTAKIH SHAK SSHHSS RSS HHLAKGHSSSSHS SSS OS C C DO 10 I=1,4 C READ(1,11) (DD(1,J),J=1.N) C 10 CONTINUE C 11 FORMAT (1OF8. 2) C C C C DD(1,J)=DEPTH AT EACH CELL OF THE OLD GRID CHRMAROTHAAERERAORSESLSKRRERSRERSKO TET SRE TEESE SSSEST SETAE THs Es COMMON/CONST/M;>N,M2.N2, DX, DY COMMON/COOR/XX (18) YY (JQ) COMMON /COGR2/XX2 (182) » Y¥2(J@2) COMMON/ COORI/XOMRTN (1, JQ), YOWRTN (18; JQ) COMMON/DEPTHS/D(1@2,J@2) ,DD(1Q, JQ) CHARACTER#1 STR READ (7590) MyNsM2,N2,ANG) XSHIFT> YSHIFT ANG=-1. 0# (ANG) READ(7,505) GRDTYP1, GRDTYP2 305 FORMAT (215) 500 FORMAT (415, 5F 10.5) ANG=ANG#3. 1415927/180.0 SCALE=1.0 14 MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN PAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN BAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN RAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN RAIN HAIN MAIN MAIN MAIN MAIN MAIN MAIN XSHIFT=XSHIFT*SCALE YSHIFT=YSHIFT#SCALE IF(GROTYP1.E@.0) GO TO 304 21 CONTINUE READ (3,31, END=999) STR» NST, NEND»A1,B1,C1 31 FORMAT‘A1, 7X, 218, 3616.11) NEND=NEND-1 IF(STR.EQ.’Y’) GO TO 20 DO 201 LLC=NST.NEND XX(LL-1)=(A1+B1¢ (ALPHC##C1) ) sSCALE 201 CONTINUE 60 TO 21 20 CONTINUE DQ 203 LLC=NST,NEND LL=LLC+1 ALPHC=LL-0.5 ALPHS=LL YY(LL-1)=(A1+B19 (ALPHC##C1) ) #SCALE 203 CONTINUE GO TO 21 999 CONTINUE 506 CONTINUE WRITE (619) 9 FORMAT (////120X," VARIABLE WAVE GRID INFORMATION’ ///) WRITE (6123) SCALE 23 FORMAT (///, EXPANSION COEFFICIENT SCALE FACTOR’, /, we SCALE=",F10.3,//) IF(GRDTYP1.E@.0) GO TQ 307 G0 TO 513 507 READ(7,501) DX,DY 501 FORMAT ‘(2F10.5) DO S11 L=1,¥ XX(L)=(L-0. 5) #DXsSCALE S11 CONTINUE DO 512 L=i,N YY(L)=(L-0. 95) #DY#SCALE 512 CONTINUE 513 CONTINUE WRITE (6) 10) 10 FORMAT (///,1X,7X CENTER DISTANCES’ »//) 11 FORMAT‘(8(14,F12.3)) WRITE (6.12) 12 FORMAT(///,1X,"Y CENTER DISTANCES’, //) WRITE (4,11) (J, YY (J). J=15N) IF(GRDTYP2.E8.0) GO TO 539 28 CONTINUE READ (4, 31,END=998) STR» NST, NEND,A1,B1,C1 NEND=NEND-1 IF(STR.E@.'Y*) GO TO 27 DO 271 LLC=NST.NEND 15 MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN HAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN MAIN 6oge% LL=LLC+1 ALPHC=LL-0.5 ALPHS=LL XX2(LL-1)=(A1+B1 (ALPHC#*C1) ) #SCALE 271 CONTINUE GO TO 28 27 ~CONTINUE DO 273 LLC=NST,NEND LL=LLC+1 YY¥2(LL-1)=(A1+B1# (ALPHC##C1) ) #SCALE 273 CONTINUE GO TO 28 998 CONTINUE G0 TO 560 539 CONTINUE READ(7,599) DX2,DY2 J00 FORMAT (2F10.5) 369 CONTINUE WRITE (4, 19) 19 FORMAT (////,20X,°VARIABLE SECOND GRID INFORMATION’, ///) WRITE (6123) SCALE IF(GRDTYP2.E@.0) 60 TO 515 60 TO 525 S15 CONTINUE DO 520 L=1,42 XX2(L)=(L-0.5) #DX2¢SCALE 920 CONTINUE DO 524 L=1,N2 YY2(L)=(L-0.5) #DY2*SCALE 524 CONTINUE 520 CONTINUE WRITE (6,40) AQ FORMAT (///,1X,'X2 CENTER DISTANCES’, //) WRITE (6.11) (1,XX2(1) » T=1,M2) WRITE (6,42) 42 FORMAT (///,1X,°Y2 CENTER DISTANCES’, //) WRITE (6,11) (Js Y¥2(J) » J=1,N2) DO 26 JJ=1,N DO 246 II=1,h XOWRTN (11s JJ)=(XX (11) -XSHIFT) #COS (ANG) + (YSHIFT 1-YY (JJ) ) #SIN (ANG) YOWRTN (11s JJ)=(XX (LL) -XSHIFT) #SIN (ANG) + (YY (JJ) 1-YSHIFT) #COS (ANG) 26 CONTINUE CALL INTERPO 99 STOP END sDECK INTERPO CHSSOKHHEAHOATHHHLAARSHLRARTATAHESASORASHRSRS HSH SSS TASS AS RAVAGE TESS c+ SUBROUTINE INTERPO Ce 16 231 wean BG BRASH PEE CARMA AKA A REAR AR ATA SHER AH ERA AHHK HRA AVAAR ARH HKO RAH AG SHREK HS HRS #CALL PARAM 10 {1 579 60 pone COMMON /CONST/M,N,M2,N2,DX.DY COMMON/COOR/XX (18), YY (JQ) COMMON/ COOR2/XX2 (182). YY2(J@2) COMMON/COORS/XOWRTN (18; JQ) , YOWRTN (12, JQ) COMMON/DEPTHS/D(1@2, J@2) ,DD(1@, JQ) DIMENSION R(KQ)s IVAL (K@) » JVAL (KQ) , DIST (K@) INTEGER MD2,ND2 DO 10 I=1." READ(1,11) (DD(I,J),J=1,N) CONTINUE FORMAT (10F8. 2) CALL POUT(1.M,1,1.N,°OLD DEPTHS (X.1)',DD,1.0,1@) JQ) DO i [=1,2 DO 1 J=1,N2 XD=XX2(1) YD=YY2 (J) K=0 IF(1.£Q@.1.AND.J.EQ.1) G0 TO 401 IF(J.NE.1) GO TO 350 IiFP=1 1FR+30 DO 599 II[=11FM, 1iFP IF(II.LE.0.0R.11.67.M) GO TO 599 DO 5 JJ=1.N K=K+1 DIST (K) =SRT ( (XOWRTN(TI, JJ)-XD) #¢2+(YOWRTN (IT, JJ)- 1YD) ##2) CS=XOWRTN(II, JJ)-XD SN=YOMRTN (IT, JJ)-YD IF(CS.GE.0.0. AND. SN. GE.0.0)R(K)=1.0 IF(CS.LT.0.0. AND. SN. GE.0.0)R(K)=2.0 IF(CS.LT.0.0. AND. SN.LT.0.0)R(K)=3.0 IF (CS. GE.0.0. AND. SN.LT.0.0)R(K)=4.0 IF(CS.E@.0.0,AND.SN.E@.0.0) 60 TO 403 IVAL(K)=I1 JVAL (K)=JJ IF(K.GT.1) GO TO 565 DHIN=DIST (1) T1=1VAL (1) Ji=IVAL (1) K1=1 IF(DIST(K).GE.DMIN) 60 T0 5 DHIN=DIST (K) kik CONTINUE CONTINUE T1=IVAL(K1) J1=JVAL(K1) Ri=R(K1) T1FM=11-15 60 TO 552 MD2=(H#1.0) ND2=(N#1.0) I7 GOYPUSUBEESESESRGSSSSRUHHS HHS SRBYRBRRARVSSSGERSAGSES 0 DO 602 [[=1,MD2 DO 602 JJ=1,ND2 K=K+1 DIST (K) =SQRT ( (XOWRTN (II, JJ)-XD) ##2+ (YORRTN ( 111, JJ)-YD) ##2) CS=XOWRTN (II, JJ)-XD SN=YORRTN (IT, JJ)-YD IF (CS. GE. 0.0. AND. SN. GE.0.0)R(K)=1.0 IF(CS.LT.0.0. AND. SN. GE.0.0)R(K)=2.0 IF(CS.LT.0.0. AND. SN.LT.0.0)R(K)=3.0 IF (CS. GE.0.0. AND. SN.LT.0.0)R(K)=4.0 IF(CS.E@.0.0.AND.SN.E@.0.0) 60 TO 403 IVAL(K)=I1 JVAL (K) =JJ IF(K.GT.1) GO TO 610 DMIN=DIST (1) I1=I1 Ji=JJ K1=1 610 IF(DIST(K).GE.DMIN) GO TO 602 DHIN=DIST (K) K1=K 602 CONTINUE T1=IVAL(K1) J1=JVAL (KL) R1=R(K1) IFH=I1-15 G0 TO 352 T1=IVAL(K) J1=JVAL(K) T1FM=I1-15 609 DiI, J)=DD(11, 31) 60 TO 717 613 SUM1=DMIN+DMIN2 SUM2=SUM1 /DMIN+SUM1 / DHIN2 SF1=SUM1 / (DHINSSUM2) SF2=SUM1/ (DMIN2*SUF2) D(1, J)=SF1DD (11, JL) +SF2*DD (12, J2) G0 TO 717 614 SUM1=DAIN+DAIN2+DMINS SUM2=SUR1/DAIN+SUM1 /DMIN2+SUM1 /DAINS SF 1=SUM1/ (DMIN®SUM2) SF2=SUM1 / (DMIN2*SURZ) SFI=SUN1 / (DMINS*SUR2) D(1, J)=SF1sDD (11) Ji) +SF2*DD (12, J2)+SF3eDD (13, J3) 60 TO 717 530 TiM4=11-4 TiP4=11+4 JiM4=J1-4 JiP4=J1i+4 DO 551 I[=11K4,11P4 IF(I1.LE.0.OR.11.G7.4) 60 TO S51 DO 553 JJ=Jin4, JiP4 IF(JJ.LE.0.0R.JJ.GT.N) G0 TO 353 60: wa 18 78 360 352 700 701 370 K=K+1 DIST (K)=SQRT ( (XOWRTN (II, JJ)-XD) ##2+ (YOWRTN (11, JJ)-YD) ##2) CS=XOWRTN (IT, JJ)-XD SN=YORRTN (TT, JJ)-YD IF (CS. GE.0.0. AND. SN. GE.0.0)R(K)=1.0 IF(CS.LT.0.0. AND. SN. GE.0.0)R(K)=2.0 IF (CS.LT.0.0. AND. SN.LT.0.0)R(K)=3.0 IF(CS.GE.0.0. AND. SN.LT.0.0)R(K)=4.0 IF(CS.EQ.0.0.AND.SN.E@.0.0) 60 TO 403 IVAL(K)=IT JVAL (K)=JJ IF(K.GT.1) 60 TO 560 DMIN=DIST (1) T1=IVAL (1) Ji=JVAL (1) K1=1 IF(DIST(K).GE.OMIN) GO TO 553 DNIN=DIST (K) K1=K CONTINUE CONTINUE T1=IVAL(K1) J1=JVAL (K1) RI=R(K1) CONT INUE DO 700 ILI=1,K R2=R(11T) IF(R2.E@.R1) GO TO 700 K2=III I2=IVAL(ITI) J2=JVAL (IIT) DMIN2=DIST (III) G0 TO 701 CONTINUE IF(R2.E@.R1) GO TO 609 CONTINUE DO 570 L=I1I,K IF(L.E@.K1) 60 TO 570 IF(R(L).EQ.R1) GO TO 570 IF(DIST(L).GE.DMIN2) GO TO 570 DMIN2=DIST(L) K2=L CONTINUE R2=R (K2) I2=IVAL (K2) J2=JVAL (K2) DO 703 JJJ=1,K RI=R (JIJ) IF(R3.EQ.R1.0R.R3.EQ.R2) GO TO 703 K3=JJJ T3=IVAL(JJJ) Ja=JVAL (JIJ) DHINZ=DIST (JJJ) GQ TO 704 19 703 704 CONTINUE IF (R3.EQ.R2.0R.R3.EQ.R1) G0 TO 413 CONTINUE DO 580 LL=JJJ+K IF(LL.E@.K1.OR.LL.E@.K2) 60 TO 380 IF(R(LL).EQ.R1.0R.R(LL).EQ.R2) GO TO 580 IF(DIST(LL).GE.DMIN3) GO TO 580 DMIN3=DIST (LL) K3=LL CONTINUE T3=IVAL(K3) J3=JVAL (K3) RS=R (KS) DO 388 ILI=1,K R4=R (111) IF (R4.EQ.R3.OR.R4.E@.R2.0R.R4.E8.R1) 6&0 TO 588 K4=I11 T4=IVAL (IIT) J4=JVAL (111) DHIN4=DIST (III) 60 TO 589 588 CONTINUE IF (R4.EQ.R3.OR.R4.£0.R2.0R.R4.E@.R1) GO TO 414 389 CONTINUE DO 590 LLL=III.K IF(LLL.E@.K1.0R.LLL.E@.K2) GO TO 590 IF(LLL.E@.K3) G0 TO 590 IF (DIST (LLL). GE.DMIN4) GO TO 590 IF(R(LLL) .E@.R1.OR.R(LLL).E@.R2.0R.R(LLL) .EQ.R3) GO TO 570 DMIN4=DIST (LLL) K4=LLL 570 CONTINUE T4=IVAL (K4) J4=JVAL (K4) R4=R (K4) D1=DAIN D2=DMIN2 DI=DMINS D4=DMIN4 SUM1=D1+D2+D3+D4 SUM2=SUN1 /D1+SUM1/D2+SUM1 /D3+SUN1 /D4 SF1=SUM1/ (D1sSUM2) SF2=SUM1/ (D2*SUM2) SFI=SUM1/ (D3sSUMZ) SF4=SUM1/ (D4*SUM2) D(1,J)=SF1eDD (11, JL) +SF2eDD (12, J2)+SF3eDD (13, J3) +SF4eDD (14, J4) 717 CONTINUE 1 CONTINUE CALL POUT(1,M2.1,1,N2, NEW DEPTHS (X,1)’,D,1.0,1@2, J@2) DO 1112 1=1,42 WRITE(2,1113) (D(1. J), J=15N2) 1112 CONTINUE 1113 FORMAT (10F8. 2) RETURN 110 APPENDIX J: SAMPLE FILES--GRID INTERPOLATION EXAMPLE 35 30) «(50 40 10.0 0.5 Figure J1. INTPGRD #1D MODS #D PARAM.3,PARAM.5 PARAMETER(10=35, JO=30) PARAMETER ( 1Q2=50 , JQ2=40) PARAMETER(KO=2000) #D INTERPO.18 11 FORMAT(15F5.0) Figure J2. INTPUPD J2 0.9 sale tne ie eter eset ee ane a) re eel le eles ome mem im cre TEC OCT LT OI a TN - HAHAHA AD An HDA TH HMA MAA AANA N OSC EO e See ee Lae et et aetna teP seh) Tet cet et et Ae cer lee sen aet lee tesose> le! ses cep ie) sap 70s cer lex, a) ye ° Oe se oe eo oe ne ee AN Sa I Ro a es ah a SSSSSSSSSASHSNSHSSHASHOTHAH GAN ABABA KRSG aa Ge Bae AHA Nn NH A Ht eK ma SSSSSSSSSSSHSNSSSSHASTSHHSSKAHSAAANS GAT AKRNHsS =) siete See eee! Ses eleretorel le tite = eS sey elena [a Sila lsesse tale ara ge aiel ses ier wieiee ANAM KH TNA aN «4 oY et te tel lse tel et eh iat se) et ae! ret et cel tal sek ten wep Je) ter jas 20) 50° 8p cep Jes ge) ie Co oe oe oe | AMVAMWAN TIN TN A Oe see. he, oe ewe SA. 8 Ge, Oe! 8, Me. te" §e- eL Ten, sey fe) > le ek Senge: ee en cep 408 Mes yey As - ANA a “= a ee ce Ce eee eee eae eee se eee aso esa Bi We ese, ie ie tele, 28, eel Tes ie) ae ° seer eres aa INTDEPO Figure J3. J3 J4 INTDEPN APPENDIX K: NOTATION a or a(x,y) ol S&S Pl ow e or c(x,y) Cy or cy (x,y) Wave amplitude function Function of the bottom slope Function of dependent variables Function of the bottom slope Function of dependent variables Wave celerity Group velocity Deepwater wave celerity Energy dissipation function Energy dissipation function Wave energy Function of dependent variables Function of dependent variables Gravitational acceleration constant Function of dependent variables Function of dependent variables Water depth Water depth at incipient breaking Wave height Wave height at incipient breaking Deepwater wave height Arbitrary subscript designating the x-direction Complex number equal to v-1 Unit vector in the x-direction Specific subscript designating the x-direction Arbitrary subscript designating the y-direction Unit vector in the y-direction Specific subscript designating the y-direction Wave number Wave length at incipient breaking Deepwater wave length Bottom slope Total number of grid cells in the x-direction Total number of grid cells in the y-direction Flow across a hydraulic jump K2 s or s(x,y) Wave phase function s Subscript denoting stable wave conditions T Wave period W Weighting factor x Coordinate direction x! Coordinate direction y Coordinate direction ir Coordinate direction Yy Water depth on the high end of a hydraulic jump Yo Water depth on the low end of a hydraulic jump a Weighting factor a* Coefficient 8 Coefficient Y Coefficient Rate of energy loss AX Grid size in the x-direction Ay Grid size in the y-direction i) Wave angle 8, Contour angle 8, Deepwater wave angle K Rate of energy dissipation coefficient ka Coefficient Ke Refraction coefficient Ky Shoaling coefficient Ws Coefficient p Water density (oj Angular wave frequency C0) Velocity potential function Mathematical symbols f) Partial differentiation V Horizontal gradient operator Vector dot product x Vector cross product | | Absolute value K3