WS Ba C GaC ied, 54a KS 77-3 UNS. oe Gag v

Figure 14 11. Due to differences in required boundary conditions between the various models, and for reasons of economy, the first 17 columns of cells along the west side of the grids (the interior area) were not used in RCPWAVE, CURRENT, and the sediment transport model. This area is covered by Model A. WIFM required the additional cells in the interior area in order to use the prototype data available there for boundary conditions and to accurately simu- late the complex tidal currents in the inlet. The Tidal Simulation Model, WIFM 12. WIFM is a general long wave model which can be used for simulation of tides, storm surges, tsunamis, etc. It allows flooding and drying of land cells near the shoreline. It is a depth-averaged model so that variations in the vertical direction are averaged in the model. It is used in the present study to determine tidal elevations and velocities in the two horizontal coordinate directions. The following description of WIFM is extracted from a report by Leenknecht, Earickson, and Butler (1984). Equations of motion 13. The hydrodynamics of the numerical model WIFM are derived from the Navier-Stokes equations in a Cartesian coordinate system (Figure 5). The long WATER SURFACE BENCHMARK CATUM Figure 5. Coordinate system for WIFM 15 wave approximations of small vertical accelerations and a homogenous fluid yield the following vertically integrated (depth-averaged) two-dimensional equations of continuity and momentum: Continuity an 0 0 ee ee (weal) ay (wel) = (7) Momentum YP du du du a gu 2 = —= —- — - + + eee ee ge Oa) tala ea VD) Cid Zz 2 2 = 6 gu,au cist neh e—iai(Q) (8) 2 2 x ox oy 1/2 ov OV OV Q) gv 2 — —+y + +e — = a + are iP Wl rev By fu + g 9 (n n,) Pa (u va) Cd Zz 2 2 cae over oy ER Ee (9) ox oy y where nN = water surface elevation above datum t = time u,v = velocities in the x- and y-directions d =n +h, the total water depth h = local still-water depth R = rate of water volume change in the system due to rainfall or evaporation = Coriolis parameter g = acceleration due to gravity Cc = Chezy coefficient for bottom friction € = eddy viscosity coefficient 16 The variable is accounts for hydrostatic water elevations due to atmospheric pressure differences, and Es and By represent external forces such as wind stress. Numerical method 14. The alternating-direction-implicit (ADI) method has been used by Leendertse (1970) and others to solve the two-dimensional equations of motion. When the advective terms are included in the momentum equations (Equa- tions 8, 9) the ADI method has encountered stability problems. Weare (1976) indicates that the problems arise from approximating advective terms with one-sided differences in time and suggests the use of a centered scheme with three time-levels. WIFM employs a centered stabilizing-correction (SC) scheme which is second-order accurate in space and time, and boundary conditions can be formulated to the same order of accuracy. A brief development of the SC scheme is presented in the following paragraphs. Note that n and h are defined at the cell center and u and v _ at the cell faces. 15. The linearized equations of motion can be written in matrix form as: Wig AUL BUY = 0 (10) where The SC scheme for solving Equation 10 is 17 k-1 k= = oO (1 + ) U (1 ne 22.) U Ci) @eaqj) tf emer ee (12) y y where 1 At i iF 2 Ax AS 1 At A == — BS SZ BY Oy The quantities Oy. and 8 are centered difference operators, and the super- script k indicates time-level. The starred quantities can be considered intermediate values between the k and k+l time-levels. 16. The first step in the SC procedure computationally sweeps the grid in the x-direction, with the second step sweeping in the y-direction. Com- pleting both sweeps constitutes a full time-step, advancing the solution from the k time-levell’ to the kt! time-level- The form of the difference equa— tions for the x-sweep is given by a qe eo we") + xs, 6. GER a) & = S (ta) = 0 (13) — (ey = oy 2 a= CG = qo) 30 (14) — Cle eye ts oF GD) = @ (15) and the y-sweep by Go eae as 7 ase (16) ysth oe (17) 18 1 k+l g k+1 k-1 — = * = = (v ve) + DAy o, (n n ) 0 (18) 17. Noting that v* in Equation 15 is only a function of previously computed variables at the k-l time-level, its substitution into Equation 18 and the substitution of u* (Equation 17) into Equations 13 and 14 yield the simplified forms x—Sweep se (ne TH) te a a + uh Tay + is s, Go) sO ~ C9) eee aha Lal lt on Meneame ee y-sweep Reena as ae a pace acc mle i ae eo ie thn i 8, sh gia, 2565 18. The details of applying the SC scheme to Equations 7-9 can be found in a report by Butler (in preparation). The diffusion terms of Equations 8 and 9 are also represented with time-centered approximations. The inclusion of diffusion terms contributes to the numerical stability of the scheme (Vreugdenhil 1973) and serves to somewhat account for turbulent momentum dissipation at the larger scales. While the resulting finite difference forms of Equations 7-9 appear cumbersome, they are efficient to solve. Application of the appropriate equation to one row or column of the grid (the "sweeping" process) results in a system of linear algebraic equations whose coefficient matrix is tridiagonal. Tridiagonal matrix problems can be solved directly, without the cost and effort of matrix inversion. 19. Apart from Courant number considerations, the computational time- step for the SC scheme in WIFM is largely governed by simple mass and momentum conservation principles. The maximum time-step for a problem is characterized by 19 At = v (23) where V is the largest flow velocity to be encountered at a cell with its smallest side length AS . The parameter n is of order 1. Therefore, the time-step is constrained by the smallest cell width which contains the highest flow velocity. In physical terms, Equation 23 requires that the flow cannot move substantially farther than one cell width in one time-step. Boundary conditions 20. WIFM allows a variety of boundary conditions to be specified, which can be classified into three groups: open boundaries, land-water boundaries, and thin-wall barriers. 21. Open boundaries. When the edge of the computational grid is defined as water, such as a seaward boundary or a channel exiting the grid, either the water elevation or the flow velocities can be specified as an open boundary-condition. This information can be input to WIFM as tabular data, or constituent tides can be calculated within the model during the time-stepping process. 22. Land-water boundaries. WIFM allows land-water boundaries to be either fixed or variable to account for flooding in low-lying terrain. Fixed boundaries specify a no-flow condition at the cell face between land and water. The position of a variable boundary is determined by the relationship of the water elevation at a "wet" cell to the land elevation at a neighboring "dry" cell. Once a water elevation rises above the level of adjacent land height, water is initially moved onto the "dry" cell by using a broad-crested weir formula (Reid and Bodine 1968). When the water level on the dry cell exceeds some small value, the boundary face is treated as open, and computa- tions for n ,u , and v are made at the now "wet" cell. Drying is the inverse process, and mass is conserved in these procedures. 23. Thin-wall barriers. These barriers are defined along cell faces and are of three types: exposed, submerged, and overtopping. Exposed barriers allow no flow across a cell face. Submerged barriers control flow across a cell face by using a time-dependent friction coefficient. Overtop- ping barriers are dynamic. They can be completely exposed, completely sub- merged, or they can act as broad-crested weirs. The barrier character is determined by its height and the water elevations in the two adjoining cells. 20 The Wave Model, RCPWAVE 24. The RCPWAVE model is a linear short-wave model which considers transformation of surface gravity waves in shallow water including the pro- cesses of shoaling, refraction, and diffraction due to bathymetry and allows for wave breaking and decay within the surf zone (the region shoreward of the breaker line). Unlike traditional wave-ray tracing methods, the model uses a rectilinear grid so that model output in the form of wave height, direction, and wave number is available at the centers of the grid cells. This avail- ability is highly advantageous since the information can be used directly as input to the wave-induced current and sediment transport models, and the prob- lem of caustics due to crossing of wave rays is avoided. The description of RCPWAVE that follows is extracted from a report by Ebersole, Cialone, and Prater (1986). 25. 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 (thus the designation mild slope equation (Smith and Sprinks 1975)). The mild slope equation can be expressed in the following form: Oia, Oa 2s fy SON a 2 Te, o x (cc, at ay (:c, oe Gone ¢=0 (24) where ¢(x,y) = complex velocity potential 27 Oo = wave angular frequency = rT T = wave period c(x,y) = wave celerity = tam Ke} = pe, lee eC) group velocity = ak k(x,y) = wave number given by the dispersion relation of = gk tanh(kh) (25) 26. Numerical solution of this equation for the velocity potential field is an effective means for solving the complete wave propagation problem. All The equation can be solved using either finite element (for example, Berkhoff 1972, Houston 1981) or finite difference methods (for example, William, Darbyshire, and Holmes 1980). Since transmission and reflection boundary con- ditions are easily implemented into these solution schemes, this approach is a popular one for modeling tsunami propagation and for solving problems involv- ing 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. 27. The model RCPWAVE is an alternative approach for solving the open coast wave propagation problem. It addresses the processes of refraction and diffraction and can be applied to a large region 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. Wave transformation outside the surf zone: theoretical basis 28. The velocity potential function for linear, monochromatic, plane waves can be represented by the following expression: ¢=ae (26) where & H(x,y) 20 a(x,y) = wave amplitude function equal to H(x,y) = wave height s(x,y) = wave phase function Here the velocity potential function describes only the forward scattered wave field. No considerations are given to wave reflections. By substituting this expression for the velocity potential into Equation 24 and solving the real and imaginary parts separately, two equations can be derived (Berkhoff (1976)), namely, 2 2 coma’ + -— + ay (v2 ° vee,)) oF a - lnalj = 0 (27) ox dy ace Ve (a°ce, Vs) = (28) 22 where the symbol V denotes the horizontal gradient operator. 29. Together, these equations describe the combined refraction and diffraction process. Diffraction is often erroneously described as the propagation of energy along wave crests which are defined to be perpendicular to the wave phase function gradient Vs . Equation 28 shows energy is still propagated in a direction perpendicular to the wave crest. Diffractive effects do change the phase function as a result of significant gradients and curvatures of the wave height. These changes cause the local wave direction to vary. If diffractive effects are neglected, Equations 27 and 28 reduce to those describing pure refraction in which the wave number represents the mag- nitude of the phase function gradient. 30. Linear wave theory assumes irrotationality of the wave phase function gradient. This property can be expressed mathematically as Vx (Vs) = 0 (29) The phase function gradient can be written in vector notation as > > Vs = |vs | cos 6@it [Vs | sin 6 j (30) > > where i and j are unit vectors in the x- and y-directions, respectively, and 0(x,y) is the local wave direction. Equations 29 and 30 can be combined to yield the following expression: 0) 0) a (|vs| sin 6) - ay (|vs| cos 6) = 0 (31) If the magnitude of the wave phase function is known, local wave angles can be calculated from Equation 31. Similarly, Equation 30 can be substituted into Equation 28 to yield p) 2 p) 2 . ae (a cc, |vs| cos 6) + aH (a cc, |Vs| sin 9) = 0 (32) 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 23 height can be determined and is proportional to the amplitude function since wave frequency is constant. 31. Equations 27, 31, and 32 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. These equations are assumed to be valid outside the surf zone. The numerical solution scheme used to solve these equations is presented in the next section. Wave transformation outside the surf zone: numerical solution 32. The three governing equations (27, 31, and 32) are solved using numerical methods. Partial derivatives within the equations are approximated using finite difference operators. Finite difference solution methods require the construction of a computational grid system or mesh. Solution accuracy is directly related to resolution within the grid system. Discussions throughout this section refer only to grid systems comprised of constant sized, rectangu- lar cells. RCPWAVE is capable of computing solutions on variably sized, rec- tilinear grid systems. 33. Figure 6 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 and N, respectively. All variables which vary as a function of space are defined at the cell centers (see Ebersole, Cialone, and Prater (1986) for details of the finite difference procedure used). 34. Model input includes values of the deepwater height Hy » direction on » and period T of waves to be simulated. It also includes 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. It is used as an initial guess for the magnitude of the wave phase function gradient. The wave celerity c and the group velocity e are functions of the wave period, wave number, and water depth. Therefore these variables can be calculated at each cell. 24 j=1TON y - AXIS i=1TOM a x - AXIS Figure 6. Definition of coordinate system and grid cell conventions used in RCPWAVE 35. From Snell's law, aa waren (88) where cy is the deepwater wave celerity (defined to be gy, an estimate of the local wave angle is obtained 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 made. The new approximation is sin(®@ - 6 ) Dee Oe Ce a6 (34) ZS) "The local wave angle, deepwater wave where 6, defines the "contour angle.' angle, and contour angle follow the angle convention shown in Figure 7. The contour angle is an input parameter for RCPWAVE. y- AXIS POSITIVE 0, NEGATIVE 6, 6 Necarive| & POSITIVE 5 x - AXIS 6, =DEEPWATER WAVE ANGLE @ =LOCAL WAVE ANGLE 6, =OFFSHORE CONTOUR ANGLE Figure 7. Definition of angle conventions used in RCPWAVE 36. Wave heights at each cell are estimated as the product of the deep- water wave height, a shoaling coefficient we and a refraction coefficient K , thus r H = HK re (35) where cos on 1/2 Kr a cos 8 (36) 26 and 1 1/2 K = —— 0.0... .C.C.:.:.:. se _ - s 2kh E + sarc | tanh(kh) (37) 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. 37. The solution scheme implements the following marching procedure once initial guesses for the variables of interest have been made. Starting at the offshore row eeionaced by i=M-3 , Equations 31 and 32 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. 38. Wave angles and heights along a given row are solved for itera- tively because of the implicit differencing formulation used. Calculations of the wave angle (actually the sine of the wave angle) and the wave amplitude function are repeated 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 sines of the wave angles and 0.001 ft (or a metric equiv- alent) for wave heights, are suggested values for prototype applications. 39. 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 27 is then used to compute the true magnitude of the wave phase gradient. This "new wave number" accounts for the effects of diffraction. Backwards differences are used to approximate the x-derivatives because they only re- quire information which has already been computed. Next, Equations 31 and 32 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 considera- tion 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 (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. ZA] 40. 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=l are set equal to their values at cells j=N-l1 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 the grid is oriented so that the y-axis is nearly parallel to bottom contours along the lateral boundaries. 41. Boundary conditions along the offshore boundary of the grid are used to initiate the shoreward marching algorithm. They are computed from deepwater 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 00 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=l) are required because of the forward marching solution scheme. Wave transformation inside the surf zone 42. Waves approaching the very nearshore zone tend to steepen and eventually break because of decreasing water depths. Shoreward of this break- ing point dissipative energy losses due to turbulence strongly influence the wave height. Linear theory does not allow for prediction of the breaker loca- tion nor for wave transformation across the surf zone. Instead, empirical and approximate methods must be used to describe the breaking process. 43. The first aspect to consider in surf zone transformation of waves is incipient wave breaking. RCPWAVE uses the following criterion of Weggel (1972): H, = ——— (38) where Hy = breaking wave height 28 1.56 fs te @ a ee) m = bottom slope hy = water depth at breaking A018. @oor™) because it accounts for bottom slope and wave period. 44. Once the incipient breaking point is defined, a mechanism is needed to transform the breaking wave across the surf zone. The transformation algorithm selected for use in RCPWAVE (Dally, Dean, and Dalrymple 1984) uses an energy flux basis. Through analogy with energy loss in a hydraulic jump in a channel, the following equation is postulated for one-dimensional transfor- mation of waves advancing in the -x direction: acre ss Goo i fee, m Gey) | on where Ec_ = energy flux associated with the breaking wave K = rate of energy dissipation coefficient (set equal to 0.2 in RCPWAVE) (Ec_) = stable level of energy flux that the transformation process 8 s seeks to attain The right side of Equation 39 is simply a dissipation term. The subscript s is used to denote the stable level of a variable. Substituting the linear wave theory estimate for E (E = 0.125 a) into Equation 39 results in the following expression: 2 d(H c_) Be Ee cu He dx hl? sg (x a) (40) 45. 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 29 H_ = Th (41) where ia I stable wave height T = proportionality coefficient (set equal to 0.4 in RCPWAVE) Equation 40 can now be rewritten as K 2 2. 2 =-|]Hec - Pla & =D 42 h g ( a oe 46. This surf zone wave transformation model, extended to two dimen- sions, can be incorporated into the conservation of wave energy equation (Equation 28) by simply adding a dissipation term D to the right side. The function D must now represent dissipation in the direction of wave prop- agation. Also for dimensional consistency, the term D must be multiplied by the wave celerity and the magnitude of the wave phase gradient, and the wave height must be replaced by the wave amplitude function. In vector notation, the energy equation becomes Vw (ace, Vs) = = ace, |Vs| - (&) rh? ce, |¥5| 5 (43) This equation can be thought of as being valid both inside and outside the surf zone. Outside, the coefficient k is zero, and the equation reduces to Equation 28. 47. All discussion relating to wave transformation within the surf zone up to this point 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 as- sumed to accurately represent the magnitude of the wave phase function gradi- ent. The linear wave theory assumption that the waves are irrotational also will be assumed to remain valid inside the surf zone. Consequently, wave angles are computed in the same manner as outside the surf zone. Details con- cerning the numerical solution inside the surf zone can be found in Ebersole, Cialone, and Prater (1986). 30 The Wave-Induced Current Model, CURRENT 48. When waves break and decay in the surf zone, in general they induce currents in the longshore and cross-shore directions and changes in the mean water level. These currents play a major role in the movement of sediment in the nearshore. They are computed using the model CURRENT. Equations of motion 49, The hydrodynamic equations used in the model for wave-induced currents may be derived from the Navier-Stokes equations (for details, see Phillips 1969 and Ebersole 1980). It is assumed in the derivation that the fluid is homogeneous and incompressible, and the vertical accelerations are negligible so that the pressure distribution is hydrostatic. By vertically integrating the three-dimensional form of the equations and applying appropri- ate boundary conditions, the depth-averaged two-dimensional form of the equa- tions of motion and continuity are obtained. These equations are derived by time-averaging over a time interval corresponding to the period of the waves. Referring to a Cartesian coordinate scheme (Figure 8), these are: Momentum = chs) 0s OT OW a g§ Magy Beg Mos g “ul x, Sy) a 0 (44) ot ox oy ox od bx od ox oy oy = 3s os oT oV OV aV an 1 1 x y 1 xy +U—+V— —+= = -- = ot u ox M oy wi oy i pd "by ne od ( ox i oy p Ox ¢ (2) Continuity an , 2 3 = : + ax (Ud) + Dy (Vd) = 0 (46) where U and V = depth-averaged horizontal velocity components at time t in the x- and y-directions, respectively, ft/sec n = displacement of the mean free surface with respect to the still-water level, ft p = mass density of seawater, silmaayizee 31 Au i} n + h = total water depth, ft € and T = bottom friction stresses in the x- and bx by 2 y-directions, respectively, lb/ft S 5 8 » and $ = radiation stresses which arise because of the xx xy Ws/ excess momentum flux due to waves (refer to Longuet-Higgins and Stewart (1964) for their significance), lb/ft T = lateral shear stress due to turbulent mixing, 1b/£t2 2S)/ a. CROSS-SECTION A-A OCEAN fe Breaker LINE BOUNDARY STILL- LINE / ee pee V. = A m A { / 6 >o0h — a { [ D > (@) ap aD Sm 4 : : | \ 2 -*— SET-UP LINE b. PLAN Figure 8. Definition sketch for an irregular beach (swl = still-water level) 32 The condition yn > 0 is known as setup, and n <0 is called setdown. 50. Bottom friction. At present, the numerical model uses a linear formulation for friction (Longuet-Higgins 1970). Thus Te 2oc <|(M |= U (47) Thy =Hoe <[uyepl? V (48) where c is a drag coefficient (of the order of 0.01) and <|u is the > eras time average, over one wave period, of the absolute value of the wave orbital velocity at the bottom. From linear wave theory 2H <|u ~ WP gin Tan |> (49) orb Equations 47 and 48 are based on the assumption that the velocity components U and V of the current are small compared with the wave orbital velocity, 6 | Be 51. Radiation stresses. The radiation stresses are of major importance since they furnish the main forces for creating wave-induced currents. Refer- ring to Longuet-Higgins (1970), for monochromatic waves, they are defined in terms of the local wave climate as follows: Seeeene | (x -5) eos Q + (n - ) eine | (50) E n cos 9 sin 9 (51) S xy S E (2n - +) ster @t+(n- ib Boaa fs) (52) yy 2 2 where okh ( Sein an (53) Nie 33 (n is the ratio of wave group celerity to phase celerity), 9 is the local wave direction (defined as shown in Figure 8), and E is the wave energy density. The values of H, k, and @ are obtained from RCPWAVE. 52. Lateral shear. In the numerical model, the coordinate scheme is chosen such that x is positive in the offshore direction and y is approxi- mately in the alongshore direction. An eddy viscosity formulation is chosen for the lateral shear. The eddy viscosity is assumed to be anisotropic. Denoting - and ey as the eddy viscosities in x- and y-directions, respec— tively, in general, - is assumed to be a function of x and y and ¢ a y constant. Accordingly, = Bae & Txy o(c, ay fi x =) ee) For field applications, the eddy viscosity Ey is chosen according to the following relation given by Jonsson, Skovgaard, and Jacobsen (1974): 2 _, ele is 2 € 7 os 0 (55) 4n h x This represents twice the value used by Thornton (1970). The value of ¢ was, in general, taken to be equal to the value of . at the deepest part (usually near the offshore boundary) of the numerical grid. Method of solution 53. In view of the similarity among Equations 44-46 and the equations for long waves (Equations 7-9), CURRENT was developed by modifying WIFM. Thus CURRENT also is an implicit finite difference model and uses the SC scheme described previously. Details of the method of solution can be found in Vemulakonda (1984). Initial and boundary conditions 54. In order to solve the problem under consideration, appropriate initial and boundary conditions must be specified. Usually an initial condi- tion of rest is chosen so that n » U , and V are zero at the start of the calculations. To avoid shock, the radiation stress gradients are gradually built up to their full values over a number of time-steps. The numerical computation is stopped when a steady state is deemed to have been reached. 34 55. The numerical model permits various types of boundary conditions among which are the following: a. "No flow" (wall). This type of boundary condition is used at FF closed boundaries such as the still-water line on beaches and at impermeable structures. The normal velocity is set to zero in this case. Io Uniform flux. In this type of open boundary condition, the flux at a boundary cell is made equal to that at the next interior cell. Thus the condition assumes 9(Ud)/ax = 0 or 9(Vd)/d3y = 0 at the boundary. This type of condition is used for the lateral boundaries since it is a passive condition. c. Radiation. This open boundary condition requires that any transients developed initially inside the numerical grid should propagate out of the grid as gravity waves. It is of the form dn/ot + c(dn/dx) = 0 where c is the phase speed of a surface disturbance n(x,t) . It is often used by the wave-induced current model at the offshore boundary and is found preferable to a wall or constant elevation condition there. Both of the latter conditions are highly reflective, and, as a result, the transients tend to bounce back and forth between the offshore and nearshore boundaries and take a long time to damp out. On the other hand, the radiation condition seems to work quite well, allowing the transients to propagate out of the grid and permitting the setdown at the offshore boundary to assume an appropriate value. 56. The boundary conditions frequently used in the wave-induced current model are illustrated in Figure 9. 57. At present, the model allows for subgrid (thin-wal1) barriers such as jetties, provided they are impermeable and nonovertopping. The program essentially sets to zero the velocity component normal to the appropriate cell face. The Sediment Transport Model 58. The sediment transport model predicts the transport, deposition, and erosion of noncohesive sediments such as sands in open coast areas as well as in the vicinity of tidal inlets. It accounts for both tides and wave ac- tion by using for input the results of WIFM, RCPWAVE, and CURRENT in terms of tidal elevations and currents, wave climate information, wave-induced cur- rents, and setups at the centers of grid cells. The model computes transport separately for straight open coast areas and areas in the vicinity of tidal inlets. In the case of the former, transports inside and outside the surf zone are treated separately. 35 SHORELINE: NO FLOW (WALL) T SW Y X UNIFORM FLUX Vid, = Voda UNIFORM FLUX V3d3 = Vada OFFSHORE: RADIATION CONDITION On 3 On = me! Or 8 Figure 9. Boundary conditions used in numerical model CURRENT Transport inside the surf zone 59. Inside the surf zone it is the wave breaking process that is primarily responsible for the transport of sediment. This process is quite complex and not well understood. There is even considerable disagreement on the primary mode (bed load or suspended load) of sediment transport in the surf zone (Komar 1978). Thus a model that determines transport in the surf zone must be empirical, to some degree, in its formulation. 60. The surf zone transport model used in this study is based upon an energetics concept developed by Bagnold (1963) who reasoned that the wave orbital motion provides a stress that moves sediment back and forth in an amount proportional to the local rate of energy dissipation. Although there is no net transport as a result of this motion, the sediment is in a dispersed and suspended state so that a steady current of arbitrary strength will trans— port the sediment. Thus breaking waves provide the power to support sand in a dispersed state (bed and suspended load), while a superimposed current (litto- ral, rip, tidal) produces net sand transport. 61. The total littoral transport rate I, (vertically integrated and parallel to the shoreline) within the surf zone can be related to the wave conditions at the breaker line by 36 I = ie) sin cos a, (56) b where I = immersed weight sand transport rate (1b/sec) K = empirical coefficient On = breaker angle and the subscript b is used to denote conditions at the breaker line. 62. Following Komar (1977), the local (vertically integrated) immersed weight longshore transport rate, per unit width in the cross-shore direction, may be written as tk, 2 a Mee (0.5f£) ogy hv, (57) where ky = coefficient to be determined f = drag coefficient y= : = breaker index Moons local longshore velocity 63. By integrating i, across the width of the surf zone Xp *b I) = f i, dx (58) 0 or “b tk 2 < 1 H I, Sea, (0.5f£) oo J h v, dx (59) under the assumption that the coefficients ky and f are constants for a particular field site. Since the values of H , ) >» and h are known, being input to the sediment model, the integral on the right side of Equa- tion 59 may be determined numerically. For example, using the trapezoidal rule, 37 2 ae i Ha te y So | ay i Bg, Yee oy 2 = Hee Ae 0 where IMAX corresponds to the number of water cells within the surf zone. Equation 60 allows for a gradual variation in cell size Ax . The velocity Vo is taken as the magnitude of the resultant of the total velocity components u, and v,, in the x- and y-directions. Thus T T Viens uw, + vs (61) where up =u +U (62) AE cals +V (63) For each computational grid line from the shoreline to the breaker line for each time-step, the value of I, is used to determine the unknown coefficient k, from Equations 56 and 59: 2 KH “e, sin Oh cos os iS ie we I, () The value of K is taken to be 0.39 if significant wave heights are used as in this study (Shore Protection Manual (SPM) 1984). 64. Once kK is known, the local transport rate i, may be determined from Equation 57 and hence the local volumetric sediment transport rate dy > as in the following equation: 2 mk, foy hv, > ey oy & se) where 0 = mass density of solids 2.65 9 for sand ir jah) u ratio of volume of solids to total volume of sediment 0.6 for sand 38 It is not necessary to know the value of f in order to solve for de in the above procedure. Once de is known, the local volumetric sediment transport rates q, and Ge for the cell may be determined by multiplying dp by Up/V» and ValVo >» respectively. Transport beyond the surf zone 65. Beyond the surf zone, waves are not breaking. Currents (tidal, littoral, and rip) still transport sediment, but the sediment load is much smaller than the load in the surf zone. Waves still assist in providing power to support sand in a dispersed state. However, there is little turbulent en- ergy dissipation, and frictional energy dissipated on the bottom represents most of the energy dissipation. Bed load is the primary mode of sediment transport beyond the surf zone according to Thornton (1972). 66. Since beyond the surf zone it is the tractive forces of currents (including wave orbital velocity currents) that produce sediment movement, a sediment transport by currents approach is taken. Again, since the complete physics of the problem is not completely understood, a semiempirical approach must be taken. In this model, the approach of Ackers and White (1973) is followed after appropriate modification for the influence of waves. 67. Ackers and White (1973) studied sediment transport due to currents. They used the results of 925 individual sediment transport experiments to establish various empirical coefficients. The approach considers both suspended load and bed load. It is assumed that the rate of suspended load transport is dependent upon the total shear on the bed. Therefore, the shear velocity v, is the important velocity for suspended load transport. Bed load transport, however, is assumed to depend upon the actual shear stress on individual sediment grains. Ackers and White (1973) assume that this stress is comparable with the shear stress that would occur on a plane granular sur- face bed with the same mean stream velocity. Thus the mean velocity of flow v is the important velocity for bedload transport. 68. Considering only currents (not waves), Ackers and White (1973) derived sediment transport rate in a dimensionless form. For convenience in practical application, this may be written as pele) Ses (66) 39 where q = total volumetric sediment transport rate per unit width normal to the current (vertically integrated combined bed and suspended sediment load CEES ECOTIES) Pp = porosity of sediment = 1 - a' D = sediment diameter which is exceeded in size by 65 percent (by weight) of the total sample n, = 1.0 - 0.2432 In Y (67) 1/3 Y=D [ees (68) v s = specific gravity of sediment y = kinematic viscosity of fluid C = exp [2-86 In Y - 0.4343 (In x)? - 8.128] (69) fra 22s n@ant 1) 1/2: Y¢ _ 9.66 m= + 1.34 (71) okval n-l v() (22 10s 224) Fe Ne (72) Re om? Equations 67, 69, 70, and 71 apply for 1 < Y < 60 (transition sediments). For values of Y greater than 60 (coarse sediments), C, n, , m, , and A 1 1 have the values of 0.025, 0, 1.5 and 0.17, respectively. 69. Beyond the surf zone, both currents and nonbreaking waves exist. So the Ackers and White formulation derived originally for currents only must be modified for the presence of waves. The waves do not increase the level of turbulence since turbulence is confined to a narrow boundary layer by the oscillating wave orbital velocities. Since the shear velocity is dependent upon the intensity of turbulence and thus the total energy degradation rather than the net traction on individual sediment grains, the shear velocity is not changed by wave action. With the wave-induced turbulence confined to a narrow boundary layer and the waves propagating essentially without energy loss, the 40 effect of waves is to increase the traction on individual grains by increasing the mean velocity felt by the grains. Thus the mean velocity of flow must be increased, but the shear velocity must remain unchanged. The mean velocity of flow is increased by using the following equation developed by Bijker (1967) and modified by Swart (1974): a 2 (v) = (v) i¢eig = (73) wave and current current 2 2; where 2) 1/2 Eo = Cy ea (74) x 10h Cc, = 18 log (4 ) (75) fw. = Jonsson's (1966) friction factor with D as bed roughness us = wave orbital velocity = <|| |> u orb Thus Equation 66 becomes 2 TY \ ah tho vil +=\F. — m poate iV ANY _G 1 qusaa—= 5 D v, = (F - A) (76) 1 A with 1-n af 1/2 1 : ae lee (es) H(z tos 2) 2ZONGZL IN: * D Loe Lier oe ee Alco (77) [g(s - 1)D] 41 Equations 76 and 77 are used for calculating sediment transport beyond the surf zone. In these equations, v is interpreted as the total velocity Vo due to currents = te + v5 and Vi is obtained from the relation 2 Ps BVe %=V es [> (78) (e) C2 VA where Pe is the bed shear stress and Cc. is the Chezy coefficient. From q , the local transport rates qe and a are obtained as before. Transport in the vicinity of inlets 70. The flow and sediment transport in the vicinity of tidal inlets differ markedly from the flow and sediment transport in the surf zone for a straight open coast. The bathymetry in the inlet area is highly irregular with the presence of channels, bars, and shoals. The breaker line is gener- ally shifted farther offshore and is irregular. Breaking and decay of waves and wave-induced currents are the major mechanisms for transport of sediment in the surf zone near straight coasts, with tidal currents being of secondary importance. Generally Up is much less than Vr: In the vicinity of inlets, tidal currents are a major mechanism comparable to wave-induced cur- rents. Moreover, Un and Vp may be comparable. We are primarily inter- ested in the transport and deposition of sediment in the navigation channel. There is no guidance in the open literature as to how sediment transport in this area should be handled. In view of the factors mentioned previously, the model uses the Ackers and White formulation modified for the presence of waves (Equations 76 and 77) in this area. From previous experience (Vemulakonda et al. 1985), this approach was found to yield satisfactory results. Erosion and deposition 71. In the case of noncohesive sediments, once the transport rates of sediment qd, and ay are known, changes in bed elevation can be determined from the continuity equation Si LS (79) 42 where & is the bed elevation. Equation 79 indicates that if more material enters a cell than leaves it, ¢ will increase (there will be deposition), and if more material leaves than enters, ¢ will decrease (there will be erosion). Equation 79 is applied in a finite difference form to all the grid cells at the end of each time-step to determine erosion and deposition. Note that an increase in ¢ means a decrease in still-water depth h and vice versa. Therefore, the values of h are updated simultaneously. 43 PART III: VERIFICATION AND BASE CONDITION TESTS Tides 72. Astronomical tides are the primary driving force for currents within St. Marys Inlet; they also contribute significantly to the ocean cur- rents in the study area. WIFM is used to compute the currents for an average tide range in order to supply the sediment transport model with a time-series of depth-averaged horizontal velocity fields covering one tidal cycle (12.42 hr for the semidiurnal tide at Kings Bay). Verification 73. Bathymetry. Most of the bathymetry and topography information used to define the grid cell elevations in Grid 1 (Figure 3) came from NOS nautical charts 11488, 11502, and 11503. Detailed soundings taken by the US Army Engi- neer District, Jacksonville (CESAJ), in June 1982 provided bathymetry for the navigation channels. All depths in the grid were referenced to mlw, and a datum difference of 3.0 ft between mlw and mean sea level (msl) was used. The maximum water depth in Grid 1 was 66 ft mlw. 74. Prototype data. The prototype tide data used to calibrate and verify WIFM in this study consisted of tidal elevations and currents. Fig- ure 10 shows the locations of the tide and velocity gages deployed in the Kings Bay study area. Tide data were collected by the United States Geologi- cal Survey (USGS) and CEWES between September and December 1982. Currents were measured along ranges 1-4 (Figure 10) on 10 November 1982, and along ranges 5-7 on 12 November 1982. These surveys recorded approximately one tidal cycle. At each range, currents were measured at three stations: A, B, and C. At each station, velocities were measured at the surface, middepth, and close to the bottom. Only ranges 1-4 lay within the bounds of the compu- tational grids, so ranges 5-7 were not used in this report. These current measurements were accurate and error-free, so they were used by WIFM in veri- fication. The details of the prototype tide and current data collection effort are reported by Granat et al. (in preparation). 75. Plates 1-4 show the measured tides at Gages 1-4 of Figure 10 for November 1982. The mean long-term tide ranges, as given by the 1982 NOS Tide Tables, vary between 5.8 ft (St. Marys Entrance, north jetty) and 6.0 ft (Fernandina Beach, Amelia River). The measured tide data for the range survey 44 “J Tes = Re NG STATE PARK = an f <2 i | Limits °7g/ACRAB! NeISLAND) VA, | 2 | vee | = = | F i OCEAN | | LEGEND SCALES | | © FRESHWATER INFLOW PROTOTYPE. a ra | | se TIDE GAGE enn 4 0 4 8 12 16 20 FT | | 2 STATION NO. | | | | | | | | | | | | | | | | | | | | | | | | | VERIFICATION STATION | LOCATION MAP |! L MEADEAY. 10-12 NOVEMBER 1982 SURVEY | Figure 10. Locations of field gages 45 date of 10 November 1982 agreed with these mean ranges and so represented an average tide for the study area. Since the prototype tides measured on 10 November 1982 represented an average tide range, these tidal elevation sig- nals were used as boundary conditions in WIFM. The prototype range current data were used to verify the velocity computations. 76. Plate 5 shows the prototype tide records for 10 November 1982. The sampling rate for the records was 5 min, and these data were spline filtered to remove high-frequency noise. Tides measured at Gages 2, 3, and 4 served as boundary conditions to the Amelia River, St. Marys River, and Cumberland Sound boundaries of the model. The signal from Gage 1, located at the south jetty of the inlet (Figure 10), was used as the boundary condition at the eastern edge of the computational grids. However, the travel time for a gravity wave between the eastern boundary and the actual location of Gage 1 is 25 min, so the boundary condition was phase shifted 25 min to account for this distance. The lateral ocean boundary conditions were interpolated between this offshore signal and the tide signal at the inlet (Gage 1). The boundary condition at St. Marys River (Gage 2) was also phase shifted 7 min to account for gravity wave travel time between the mouth of the river (the grid boundary) and the site of the prototype gage farther upstream. 77. The zero datum shown in Plate 5 represents the mean for each measured tide record rather than a geophysical datum such as the National Geodetic Vertical Datum (NGVD) of 1929 . The elevations of the tide recorders used in this study were not referenced to a benchmark, so the relationships between the gage means are not known. The lack of a common datum caused numerous problems during calibration, since WIFM requires all elevations to be measured from a common datum. Since the tide gages were all fairly close to one another (less than 2 miles apart), even minor changes in elevations caused gradients great enough to change the flow patterns within the study area. These elevation adjustments were determined during the model calibration. 78. Permeability of jetties. Since both jetties at St. Marys Entrance are awash at high tide and known to be permeable, the tidal model has to prop- erly simulate this effect on the velocity patterns. From field measurements taken by Florida Coastal Engineers in 1975, "it was estimated that up to 28 percent of the total [tidal] flood flow enters [the inlet] through the per- meable jetties rather than at the ocean terminus of the structures." (Parchure 1982, p. 27). Since the widths of the jetties are small compared with grid 46 cell dimensions, they can be modeled in WIFM as flow barriers placed at grid cell faces. The hydrodynamics of flow over these barriers is computed by the broad-crested weir formula (Chow 1959). The parameters of barrier submergence (head across the weir) and Manning's n in the formula dictate the flow rate or "permeability" across a barrier in WIFM. The permeable jetties at St. Marys Entrance were therefore simulated with submerged barriers in the tidal current model. 79. An ad hoc method determined barrier "permeability" parameters for WIFM. Two initial assumptions were made to reduce the number of variables involved in parameter estimations. First, the crest of the submerged barriers used in WIFM was arbitrarily set to -4 ft msl. This depth ensured that the barriers would not become exposed during low tide. Second, it was assumed that the bottom friction in the study area, below -10 ft msl, could be approximated with a set Manning's n of 0.025. These assumptions reduce the variables affecting permeability to: (a) water velocity over the barrier, (b) water depth surrounding the barrier, and (c) the Manning's n of the bar- rier. The relationships between these variables were determined by a simple computational experiment. 80. A horizontal flume with length scales of the same magnitude as St. Marys Inlet was modeled by WIFM. The flume is 16,000 ft long and 2,400 ft wide, and it has a submerged barrier obstructing half the channel width at the center of the flume. Plate 6 illustrates the plan view of the layout, and the velocity pattern for a typical computation. WIFM was run for 128 different combinations of flow velocity (1, 2, 3, and 4 fps), water depth (10, 20, and 30 ft), and barrier Manning's n (varied from 0.025 to 0.050). Discharges per unit width were measured at the inflow and over the barrier for each run, and the permeability for the given conditions was computed as the percentage ratio of the latter to the former. It was determined that permeability was not a function of the flow velocity. 81. Figure 11 shows the family of curves plotted from this experiment. To set a desired permeability for a jetty barrier in the tidal current model, the water depth at the jetty section is noted, and the appropriate Manning's n is determined by interpolating between isobath curves in Figure 11. The Manning's n values needed to simulate a 28 percent jetty permeability were determined for each barrier segment in this fashion. 47 JETTY PERMEABILITY PERCENT PERMEABILITY a fo) 20 10 0 1 2 3 4 5 6 1 8 9 10 " BARRIER CHANNEL Figure 11. The relationship of barrier permeability to depth and Manning's n 82. Calibration of the tidal model required the adjustment of WIFM boundary conditions until the computed elevations at tide Gage 1 matched the prototype data for 10 November 1982. The model was then verified for correctness by successfully reproducing the velocities measured at ranges l, 3, and 4. The WIFM boundary conditions were adjusted during calibration by adjusting the datums for the prototype tide signals and accounting for the phase differences in the signals due to their placements in the grid as input conditions. All of the datum adjustments were less than 2 in. Note that WIFM used a time-step of 60 sec for all the computations. 83. Plate 7 shows where numerical gages were placed in Grids 1 and 2 in order to measure the computed velocities for the base and plane conditions in St. Marys Entrance. The gage sites in Plate 7 all correspond to either loca- tions where prototype data were collected during the survey of 10 November 1982, or to important locations in the navigation channel. Table 1 equates the gage numbers in Plate 7 with the gage names used subsequently. The 48 missing numbers in the sequence correspond to gages outside the grid segment shown in Plate 7. 84. Plate 8 shows the match between the computed and prototype tide for 10 November 1982 at the four gage locations. The computed signals at Gages 2-4 are merely the prototype tide with the datum adjustments added, since these gages are boundary conditions in the model. Computations for tide Gage 1, in the inlet, match the prototype data. 85. Plates 9-13 compare the model computations of tidal currents to the prototype surface and middepth velocities at ranges 1, 3, and 4. (Solid curves represent numerical results and dashed curves prototype data.) Varia- tions with time of both velocity magnitude and phase are shown over a tidal cycle. Since the numerical model is depth-averaged, in general its results would match the middepth measurements more closely. The agreement between the computations and the prototype data at the inlet (range 1) is excellent, both in magnitude and phase. The ability of the tidal current model to simulate the inlet velocities is crucial to the other aspects of this study, and the model performs this task well. In the case of ranges 3 and 4 (Plates 10-13) the numerical results represent the whole range. The computed and prototype velocities at range 4 (Cumberland Sound) also agree well. The velocity com- parisons at range 3 (St. Marys River) agree in magnitude but differ slightly in phase. This phenomenon is probably due to the drainage characteristics of large marsh areas around St. Marys River which lie outside the boundaries of the tidal model. 86. Plates 14 and 15 show the computed velocity patterns in St. Marys Entrance for the peak flows of ebb and flood tide. The dashed portions of the barriers represent the permeable sections of the inlet jetties. The flow across the jetties can be seen on these Plates, and it appears that the flow is more pronounced across the south jetty. 87. In summary, the tide model used prototype gage elevation data for forcing boundary conditions. The measured tidal elevation at the south jetty of the inlet was reproduced in the numerical model. There was good agreement of numerical results with measured velocity data at range 1 in the inlet and satisfactory agreement at interior velocity ranges. Where the flows are influenced by other features in the region interior to the inlet, such as marshes which are not included in the tide model of Model B, close agreement is not expected. This lack of agreement should not cause concern since the 49 interior flows are studied by Model A and since the main purpose of Model B is to study coastal processes in the region mostly exterior to the inlet. There- fore, the calibration and verification of the tide model are complete and successful. 88. Since the channel bathymetry and geometry used in verification tests are close to existing (base) condition and the tide of 10 November 1982 is representative of the mean tide, the results of WIFM from verification tests were also taken to be those for base condition. They were used accord- ingly in the sediment transport model. The reader should note that the tidal conditions of 10 November 1982 were used in Model A also for base condition. The tide model generated a data file, consisting of tidal elevations and velocities, for each grid cell for each half hour of an approximated semi- diurnal period of 12.50 hr for later use in the sediment model. Waves and Wave-Induced Currents 89. The hydrodynamic models RCPWAVE and CURRENT were extensively tested and compared with analytic solutions, laboratory data, and available field data during their development (Ebersole, Cialone, and Prater 1986 and Vemulakonda 1984). Considerable experience has been gained previously at WES in field application of these models (Vemulakonda et al. 1985). So reliance can be placed on the results of these models. The models do not require site- specific calibration. Because synoptic field data on waves and wave—induced currents were unavailable for the project area, no separate verification tests were performed for these models except indirectly through sediment model veri- fication. The models were run for the base condition using the same bathyme- try and channel geometry as in the tidal model. The results of the models were used in verification and base tests of the sediment transport model. Wave climate 90. One of the primary objectives of the wave and wave-induced current model runs is to furnish input to the sediment transport model. In the case of the sediment transport model, the interest is in sediment transport and yearly shoaling rates in the navigation channel under an average year's wave climate, including normal storms but excluding extreme storms such as hurri- canes and other tropical storms. So the wave climate for an average year at the project site was obtained from the WES Wave Information Study (WESWIS) 50 based on 20-year hindcast. This information was in the form of frequency of occurrence of waves in terms of predominant direction, significant wave height, and period bands in a depth of 60 ft mlw. Table 2 shows a sample of WESWIS data for St. Marys Inlet. The wave approach angle notation in this table is different from that used in the rest of this report. Angles in the table are measured with respect to the shoreline. Consider waves with an ap- proach angle of 70.0 to 79.9 deg and significant wave heights in the band 0.0 to 0.49 m. They are distributed in period bands between 0.0 to 11.0 sec and greater. The total frequency of occurrence of these waves summed over all the period bands is 3.515 percent (3,515 + 1,000) or 0.03515. Similarly, WESWIS provides wave information in direction bands of 10 deg from 0 to 180 deg for all the wave height bands (0 to 5.00 m and greater). 91. In this study, these data were further consolidated into 79 differ- ent incident wave conditions (combinations of significant wave height, period, and direction) to run the wave and wave-induced current models. For conve- nience in running the sediment transport model, wave condition 80 was defined as a null wave condition when there was no significant wave activity. These combinations are listed in Table 3 which shows the percentage of occurrence of each condition. The directions represent angles in degrees measured from azi- muth 87.5 deg (approximate shore normal direction). Negative angles signify waves coming from directions south of the normal; positive anglés signify waves coming from directions north of the normal. The wave combinations shown in Table 3 are obtained from Table 2. Consider the example from Table 2 again. Since the wave approach angle is between 70.0 and 79.9 deg, the aver- age value of 75.0 deg is taken. In terms of the notation of Table 3, the wave direction becomes -12.5 deg. Since the wave height band is from 0.0 to 0.49 m, the mean value of 0.25 m or 0.82 ft is taken for the significant wave height. As for period, on the basis of the distribution of Table 2, a mean period of 8.0 sec is taken. These are the values shown for wave 28 in Table 3. Jetties 92. To account for diffraction of waves due to the two jetties of St. Marys Inlet, a special subroutine was developed. It used the diffraction solution of Penney and Price (1952). The wave model was first run without accounting for the presence of the jetties. The diffraction subroutine took the solution near the jetties as input and modified it to allow for 51 diffraction around the jetties. For this, the actual layout of the jetties is used. The procedure was somewhat similar to that of Perlin and Dean (1983). During the development of the subroutine and the procedure, several tests were performed including comparison of its results to the laboratory data of Hales (1980) for a single structure case, and to two physical hydraulic model tests conducted at CEWES for the two jetty case. In each case, the results of the subroutine compared favorably with laboratory data. In the grid for CURRENT, the jetties were represented in a stair-step fashion similar to that in WIFM. CURRENT treated them as thin-walled nonovertopping impermeable barriers. 93. Because of the highly variable nature of the computational grid, the wave model was run on a uniform grid with 500-ft by 500-ft cells, and its results were interpolated to the variable grid. The wave and wave-induced current models were run for each of the 79 wave conditions. There are no waves or wave-induced currents corresponding to wave 80. Each of the wave conditions represented the offshore boundary condition for the wave model. The model was run for the condition, and its results were stored in the form of wave height, direction, and wave number at each grid cell. They were next used as input to CURRENT which computed and stored on a file the setup nN and the two velocity components U and V for each grid cell for each wave. For convenience the corresponding wave information for each cell was also stored on the same file. Note that in general CURRENT used a time-step of 50 sec and in each run calculations were continued until an approximate steady-state con- dition was reached by the current field. Results 94. For convenience, results for only three typical cases out of the 79 listed in Table 3 will be presented here. They have been selected so that they represent waves coming from south and north of the shore-normal direction and approximately along the shore-normal direction. It is convenient to pre- sent the results from the wave and wave-induced current models in terms of the uniform grid in the computational plane rather than the variable grid (Fig- ure 3). One advantage of this type of display is that the results for the entire grid can be shown on an 8-1/2-in. by 1l-in. sheet of paper. However, there is a disadvantage in that cell centers are not at the proper distances relative to each other. Thus, boundary cells appear much closer to the center than they really are. Moreover, the cell dimensions are distorted. Cells close to the inlet, the barrier islands, and the navigation channel appear to 52 be relatively larger; and as one moves away from this region (for example, closer to the lateral and offshore boundaries) the cells appear to be rela- tively smaller than they really are. In what follows, for convenience, the results will be shown on the uniform grid. 95. Figure 12 shows the region covered by the 50- by 73-cell uniform grid in the computational plane. The grid is 50 cells wide in the alongshore 75 N 70 | AMELIA NY . AZIMUTH ISLAND 65 60 55 50 45 40 35 30 25 0 8 16 24 32 40 48 Figure 12. Uniform grid and bathymetry in computational plane direction and 73 cells long in the onshore/offshore direction. The figure shows Amelia and Cumberland Islands, the navigation channel, the locations of the two jetties on St. Marys Inlet (the jetties are stair-stepped for the CUR- RENT model), and bathymetric contours with elevations referenced to msl (mlw plus 3 ft). The offshore boundary of the grid is at an approximate depth of 63 ft msl. Note the shoals offshore, south of the south jetty, and north of the north jetty. For convenience, these will be referred to hereafter as the offshore, south, and north shoals, respectively. 53 96. Figures 13, 15, and 17 display the results of the wave model, at cell centers, corresponding to waves coming from three different directions. These are waves 22, 45, and 59 from Table 3. These three conditions will be referred to as cases A, B, and C, respectively. For all three cases, the significant wave height in 63-ft depth of water msl is identical and equal to' 7.4 £t. The period is roughly the same. The wave directions are quite different. In each of the figures, the length of an arrow (vector) is proportional to the wave height (a scale is shown), and the direction of the arrow indicates the direction in which the waves are progressing. For clarity, only vectors for alternate cells in each coordinate direction are plotted. 97. Figures 14, 16, and 18 present the wave-induced currents at grid cell centers corresponding to cases A, B, and C. In these figures, the length of an arrow is proportional to the magnitude of the current (a scale is shown), and the direction of the arrow indicates the direction of the current. The currents are depth-averaged. For convenience and clarity, only vectors in alternate cells in each coordinate direction are plotted. 98. Figure 13 corresponds to a wave of period 7.2 sec coming from azimuth 120 deg in 63-ft depth msl (Case A). The waves respond to the off- shore shoal. The wave height increases, and the wave direction changes as the waves go over the shoal. The wave height decreases, and the waves resume their original direction once the waves pass the shoal. The waves converge on the south shoal due to refraction, move parallel to the jetty, and break on the shoal. Because of the sheltering effect of the south jetty, very little of the incident wave energy goes past the jetty tips into the inlet. Note also the sheltering effect behind the north jetty resulting in very little wave action there. The waves converge on the north shoal, and the wave energy spreads out (diverges) due to a "bay" effect as the waves reach the shoreline of Cumberland Island. Near the approximately straight shorelines of both bar- rier islands, the wave height decreases because of wave breaking and decay. 99. Figure 14 shows the wave-induced currents corresponding to Case A. Near the straight part of the shorelines of Amelia and Cumberland Islands, the currents are mainly parallel to the shore and move to the north. However, near the south shoal, because of wave refraction and breaking, the currents tend to move in a westerly direction. The net result is the counterclockwise circulation we see over the shoal. The currents are the largest in this 54 PLOY OF WAVE DIRECTIONS AMD WAVE HEIGHTS (KBUUV2e2) AMELIA i b CUMBERLAND {} . ISLAND ua C ISLAND U Ve hii, * iyi, YY : Me ues 2 Be Bl = 74 Be, 1S 762 S85 35 Yt Azimuth = 120 deg YY “n Liat ey Hy, HE 40 48 PLOT OF VELOCITY (KBUCee3) i AMELIA ay CUMBERLAND ISLAND | or ISLAND Figure 14. Wave-induced currents for Case A G \>! a a i St wy Oe 1 a 52) PLOY OF UAVE DIRECTIONS AND VAVE HEIGHTS (KBUUU4ED U NOW ean Sf % AMELIA ISLAND CUMBERLAND ISLAND 65 ! i a R 60 if UY a! Art | ay 3 1! In Y 50 ‘5 | \ al 4 \N fi a4 45 hk \ Ni 40 R x 35 4 4 | x el Ke 25 i Hf ¢ & 20 Fe [ L BY 15 10 5 0 Oo § 16 «24 32 40 48 PLOT OF VELOCITY (KBUC4S3) AMELIA ISLAND c& 7 ? a zat, Arie Soy Figure 16. Wave-induced currents for Case B Iyveyeourr eda eaoa tee Somes ay Pee ee vs >> bee NN R i t a \e A \' ‘ iret | | ad Ig C2 Add IG aG>v72x2424vaasa awa FIM ITT eacy/! 9 rary fay 4 > La at oe St ee 44a ») 9 Tt 2 SI a ey a a > 2 2 > ? 2 ? > > > > > > > > Figure 15. Wave heights and directions for Case B, BS 74 aes WS Pos SGC5 Azimuth = 80 deg SFT/SEC toeaageyvvuvvyvwvy awvwyvrvwrwvwvvevvvwevwvw vwv vv v 2 CUMBERLAND ISLAND PLOT OF UAVE DIRECTIONS AND VAVE HEIGHTS (KBUUUG9) Pomme cee a esti z iS ISLAND a> > al y | Hs 4 Tt ag ARS * h aN \ Figure 17. Wave heights ‘\ ea XA ¥ pel hecton Fore > = ER ANSE Aeaencn = 80 den ANA He cr : ARRAN VAAN ARS oe : RAR 0 8 16) 2h 2 a 70 AMELIA 65 |. ISLAND 60 55 2 Figure 18. Wave-induced 40 sis currents for Case C 30 + Pea ee ea . tl InP > VY pnw part anrAanarhee 57 region. Currents are strong on the inside of the north jetty because waves advance and break along the jetty. These currents have a westerly direction and advance into the inlet. Because of diffraction, currents are very weak behind the north jetty. 100. Figure 15 corresponds to a wave of period 7.8 sec coming from azimuth 80 deg in 63-ft depth of water msl (Case B). In this case, since the waves are approximately normal to the shoreline and the offshore contours, there is not much refraction of the waves offshore or even near the straight line portion of the shoreline. The waves converge on the south shoal, because of refraction, resulting in higher wave heights on the shoal. There is a similar convergence on the north shoal and a small divergence of wave energy near Cumberland Island. The incident wave direction is such that there is very little sheltering due to the two jetties. As a result the waves propa- gate straight and far into the inlet because the depth contours are approxi- mately straight and parallel to the waves inside the jetties. The wave heights are large between the jetties. 101. Figure 16 displays the wave-induced currents for Case B. In this case, because the incident waves are approximately normal to the shoreline, there are no noticeable currents along the straight portions of the shoreline. Because of wave convergence and breaking, the currents are strong over the south shoal. A circulation pattern may be observed on the shoal. As the waves propagate straight and unchanged between the jetties without breaking or decaying, there are no noticeable wave-induced currents in this region. Cur- rents may be observed on the north shoal because of wave convergence, break- ing, and decay there. These currents are smaller than those observed on the south shoal. 102. Figure 17 corresponds to a wave of period 6.9 sec and azimuth 60 deg in 63-ft depth of water msl (Case C). The waves refract on the off- shore shoal. They refract and converge strongly on the north and south shoals, resulting in higher wave heights on both shoals. Since the waves are aligned approximately parallel to the two jetties, there is very little sheltering due to the jetties so that the waves propagate deep into the area between the jetties. They break and decay near the straight portions of the shoreline. 103. Figure 18 represents the wave-induced currents for Case C. Near the straight reaches of the shoreline the currents are parallel to the shore 58 and in the southerly direction, as one would expect. The currents are strong over the north and south shoals because of wave breaking and decay. The pat- tern of the currents is complicated. Currents move in an easterly direction along the interior of the north jetty and westerly direction along the interior of the south jetty. 104. In summary, the overall results of the wave and wave-induced cur- rent models used for verification and base conditions are reasonable and behave in a manner one would expect, given the complicated bathymetry of St. Marys Inlet region and the two jetties on the inlet. The incident waves respond differently to the bathymetry, the shoals and the jetties, depending on their direction of incidence. The wave-induced currents depend on the bathymetry, the waves everywhere in the grid, and whether or not the waves break and decay in a given region of the grid. Sediment Transport Verification tests 105. In order to make a strict verification of the sediment transport model, it is necessary to have either long-term (several years long) informa- tion on shoaling rates in the navigation channel and bathymetric changes in the general area or actual wave measurements made simultaneously with measure- ments on shoaling rates and bathymetric changes over a shorter time period (a few months). The latter type of data are not available for the project area. As for the former, examination surveys are available for the channel. As men- tioned previously, the approach used by the sediment transport model does not account for extreme storms. So the prototype data selected should not include periods of such storms. As for dredging, it is possible to simulate dredging in the numerical model provided detailed information is available on the loca- tions and durations of dredging and the amounts of material dredged at each location. Usually, such detailed information in terms of computational grid cells is not available from dredging records. Therefore the prototype data should not include periods of dredging. In the case of St. Marys Inlet, the navigation channel was deepened to the existing condition (40-ft project depth) in 1978 and 1979 so only 5 to 6 years of prototype data are available. The channel still has not stabilized after the deepening. Sediment transport and other processes continue to be in a state of transition. Out of the 59 available information on examination surveys for the navigation channel, we were able to locate only one set of examination surveys covering a period of approximately 1 year (1980 through 1981) which was free from the effects of dredging and severe storms. The duration of this data set is too short for the data set to be used for strict verification of Model B results which are based on 20-year hindcast wave data. Therefore, a strict verification of Model B results with the data set is not possible. Instead, the average yearly erosion/deposition rates along the channel obtained from the data set will be compared with Model B results to see if the numerical model results are reasonable and agree with the trends and shoaling magnitudes exhibited by the field data. 106. Prototype data. The field data set consisted of seven examination surveys conducted by CESAJ during 1980 and 1981 between sta -80+00 and sta 325+00 (Figure 19). For convenience, this pre-1985 CESAJ stationing will be used throughout this report. The locations and dates of the surveys are oy s/ ma 399+73.92 325+00 201+00 (APPROXIMATE LOCATION OF JETTY TIPS) 130+00 -80+00 PLAN 1 EXTENSION se -97+76 ! Figure 19. Pre-1985 CESAJ stationing 60 shown in Table 4. On the basis of several tests, it was determined the datum used in survey 2 was in error by 0.5 ft. This is not surprising since the reach of channel surveyed was far away from the tide gages used to locate the datum. The datum for this survey was adjusted accordingly. 107. The field data were examined in two ways. First, surveys l, 2, and 7 were used to determine average yearly erosion/deposition rates. At each of the 35 locations along the channel corresponding to computational grid cell centers, depths across the width of the channel were averaged, and the erosion/deposition rates were computed and extrapolated to feet/year values. (Following a similar procedure, but computing the average depth for each cell from 16 spatially distributed points in the cell, yielded results that were close to the results obtained from averaging the cross-section depths). Next, the total period was broken down into three separate periods of approximately 4, 2, and 6 months, based on the survey dates. At each of the 35 locations, the erosion/deposition rates obtained for these periods were converted to feet/year values, and the extreme values at each location were determined. Figure 20 is a plot of the average and extreme values from the prototype data -15 LEGEND nN — PROTOTYPE AVERAGE / \ A - ! \ ——— PROTOTYPE EXTREMA gw / MI VIM 4 on EROSION ~<+* DEPOSITION RATE, FT/YEAR (a) — f=) 15 -100 -50 0 SO pan Ome O0ie a 200Ria250e S00 350 DISTANCE, 100 FT Figure 20. Prototype data on erosion/deposition rates 61 at different stations along the channel. The sign convention that erosion rates are positive and deposition rates are negative is used hereafter. 108. Testing procedure. At the start, the sediment model used the bathymetric information from field surveys 1 and 2 for the channel. Outside the channel, the bathymetry used was identical to that used by the tide, wave, and wave-induced current models for base condition since better detailed information was not available. 109. To generate a wave sequence for 1 year for the verification and base tests of the sediment model from the waves given in Table 3, the follow- ing procedure was used. Each wave event in the sequence was assumed to be steady with a duration of 4 hr. This is a reasonable assumption from field experience and measurements, provided extreme storms are ruled out as done here. Each wave condition (1 to 80) of Table 3 was identified with a fre- quency of occurrence. During the running of the sediment model, wave condi- tions were selected such that each of the 80 conditions occurred at the frequency shown in Table 2. Thus, the waves used by the sediment model re- flected nature in terms of wave statistics provided by WESWIS. The same waves were used for base and Plan 1 tests. 110. The sediment model used a time-step of 1 hr. This value was considered optimum on the basis of testing and previous experience. The computational sequence employed by the sediment model consisted of the fol- lowing steps: a. Read in the local bathymetry. b. Pick the first wave condition. c. Read in the corresponding wave information (wave height, angle, period, wave-induced velocities, and setups/setdowns). . Read in the first hour of the tide data (tidal velocities and elevations). - Combine the above quantities to obtain a total velocity field, wave field, and local depth. f£. Compute sediment transport quantities and the associated ero- sion and deposition rates. g- Repeat steps d, e, and f at 1l-hr intervals for a total of 4 hr. h. Pick the next wave condition and continue steps c through g, Gie@o As indicated previously, the local still-water depth h for each cell was updated at each time-step based on the erosion or deposition in the cell. The 62 total local depth, which is the sum of h , ", and 1 , was also updated. The total velocity components Up and Vr were adjusted on the basis of sim- ple continuity to account for the change in bed elevation of the cell. It was observed from running the sediment transport model that model results in terms of erosion/deposition rates (ft/year) along the channel became approximately constant after the model was run for 150 to 180 prototype days. There were minor variations from run to run as the total time was increased, but the trends and magnitudes stabilized. Therefore, the above sequence was performed for 180 instead of 365 prototype days to compare with field data for verification. 111. Results. Based on the trends exhibited by the prototype data, the reach of the channel between sta -—80+00 and sta 325+00 was divided into seven zones for verification (Figure 21). A similar approach was used for Model A verification. Four to six computational grid cells were in each zone. The value assigned to a zone is the average of the values for the cells in the zone. A comparison of the prototype average erosion/deposition rates with results of Model B is shown by zones in Figure 22. Also shown in the figure are prototype extrema based on 1 year of prototype data. Model B results show the same trends as the prototype average results and are in approximate quantitative agreement in zones 1-4 (between sta -80+00 and sta 241+56). It is not surprising that they do not match quite as well between sta 241+56 and sta 325+00. This is a highly dynamic region, especially outside the jetty tips (sta 251+00) and is very much dependent on the actual (rather than aver- age) wave climate that existed between surveys. This can be seen in the large spread between prototype extrema. There is movement of material from the off- shore bar and shoals into the channel. As was pointed out previously, proto- type data of 1 year's duration are not necessarily representative of a 20-year average. On the whole, Model B results are reasonable and in agreement with field data. Base tests 112. The only difference in the bathymetries used at the start of veri- fication and base tests was in the navigation channel. The sediment model used the channel bathymetry from the CESAJ survey of June 1982 for the base tests because the same bathymetry was used in all the other models for base condition. 63 DISTANCE, 100 ft Figure 21. Zone numbers assigned to channel reaches for verification tests EROSION +> DEPOSITION RATE, FT/YEAR a LEGEND oa | oleae PROTOTYPE AVERAGE a \ ne a —-« PROTOTYPE EXTREMA, a o—o \ by MODEL B vy) 25 0 25 5.0 78 -100 -50 0 S000 SOR e e008 e250 eS SOC hearS50 DISTANCE, 100 FT Figure 22. Comparison of prototype data with Model B results for verification 64 113. At the time Model B computations were made, up-to-date field sur- vey information was not available on channel bathymetry between sta 325+00 and sta 399+74, nor was up-to-date bathymetric information available for areas on either side of the channel. Model B used the best available information, which usually was CESAJ construction dredging survey information and the bathymetric information from NOS charts. Unfortunately, this information does not seem to represent the current bathymetry for the reach of the channel be- tween sta 325+00 and sta 399+74 and the areas of either side of the channel in this reach, according to the latest CESAJ surveys. These surveys seem to indicate that the depths may be greater (by 5 ft or more) in this reach. For this reach of the channel, the information available to us at the time of com- putations indicated the depths were greater than the existing project depth of 40 ft and that the channel seemed to be in a state of erosion; therefore it did not require maintenance dredging. There was no quantitative information available on erosion/deposition rates for this reach. 114. The sediment transport model followed the same testing procedure as it did for verification. The model was run for 200 prototype days, and its results were converted to channel erosion/deposition rates (ft/year). For base tests, the entire length of channel offshore of sta 399+74 was consid- ered. The channel was divided into ten zones (zones 1 to 10 in Figure 23). Figure 24 shows the erosion/deposition rates by zone for base. When the results for verification and base are compared (Figures 22 and 25), it is observed that there is similarity in the trends and magnitudes. This is not surprising since the channel bathymetry in the two cases is not that much -100 -50 0 SO 1000 150i 2002500 300) 350400 DISTANCE, 100 ft Figure 23. Zone numbers assigned to channel reaches for base and Plan 1 results 65 different inside the jetties and the forcing functions (tides, waves, and wave-induced currents) are the same for both cases. In both cases, there is deposition outside the jetty tips (sta 251+00). It changes to erosion inte- rior to the jetty tips because of circulation due to wave-induced currents. The heaviest deposition rates are observed near the jetty tips. This is the area where the channel cuts through the offshore bar and material from the bar tends to move into the channel and deposit there. -100 -50 0 50 100 150 200 250 300 350 400 DISTANCE, 100 ft Figure 24. Erosion/deposition rates (ft/year) for base condition from Model B (+ = erosion, - = deposition) 66 EROSION ~+e DEPOSITION RATE, FT/YEAR oS 0 Figure 25. 90 =6 100 = 150 3 200 3s 250~S 300 DISTANCE, 100 FT Erosion/deposition rates for base 67 350 400 PART IV: PLAN CONDITION TESTS Paltaniwel! 115. Model B tested only one plan condition which will be referred to hereafter as "Plan 1." The plan is to (a) widen the navigation channel to 500 ft, with the widening taking place on the north side of the present entrance and offshore channels; (b) extend the channel on the ocean side, with the extension being at an angle 20 deg south of the present channel center line at sta -97+76 approximately; and (c) deepen the channel to -49 ft mlw (46-ft project depth plus 3-ft advance maintenance). The channel is to have a trapezoidal cross section with side slopes of 3H:1V. Figure 26 shows details of the planned channel layout and cross section. As requested by the Officer In Charge of Construction (OICC), TRIDENT, the plan tested assumes also that the landward 1,000 ft of the south jetty will be made sand-tight simultaneously. 116. In view of the urgent need expressed by OICC for Plan 1 results from Model B for design of the entrance and offshore channels, the wave and wave-induced current models were not rerun for the Plan 1 condition as origi- nally planned. Running the models again would have delayed the results con- siderably. Moreover, since the changes from base to Plan 1 condition of the navigation channel were reflected mainly in the cell size and bathymetry for one row of cells in the computational grid, it was felt the effect of channel modification on waves and wave-induced currents would be minor compared to its effect on tides and sediment transport. Computational Grid 117. As indicated previously in Part II, the computational grid for Plan 1 (Grid 2) retained the major features (overall dimensions, orientation, number of cells, etc.) of the grid for base (Grid 1). The only difference between the two grids lies in the mapping of the row of cells corresponding to the navigation channel. These cells were made 500 ft wide by minor adjust- ments of the cells on either side. In view of the rectilinear nature of the grid, the navigation channel was represented in a stair-step fashion where it turned south. It was assumed that dredging for the navigation channel 68 Teuueyo [T uetTg Jo s{TrTe,eq NOILOAS SSOYD Le =0 ‘oz ean8ty l SATIN IWOIILNWN fanvisi Ae day : | VITA anv yaa) oN ‘ B 69 extension stopped wherever the natural ocean depth became equal to or greater than 49 ft mlw. (This location of the oceanward entrance of the navigation channel would be determined in the field from the latest bathymetric surveys for the final channel design.) In the navigation channel itself, the planned channel depths were used. The bathymetry used outside the channel was the same as that for base condition. Tides 118. To properly model the sand-tightened section of the south jetty in the numerical model, the crests of the barriers simulating this jetty section were raised to the prototype jetty elevation of +3 ft msl; and the Manning's n values governing flows over the barriers were changed appropriately. 119. Plates 16-19 compare the computed base and Plan 1 velocities (magnitudes and phases) at seven sites in the inlet (refer to Table 1 and Plate 7 for locations of these sites). All of the changes in tidal currents are due to sand-tightening of the south jetty. The peak velocity at tide Gage 1 (Plate 16) has increased by approximately 10 percent between base and. Plan 1 due to sealing of a section of the south jetty. The gages at the throat of the inlet (Endeco velocity Gage 2, range survey Gages 1-A, 1-B, and 1-C, and Fort Clinch) (Plates 16-19) show negligible change in velocity. The velocity at the ocean end of jetties (Plate 18) increases by about 10 percent in both ebb and flood for Plan 1 and shows a slight phase shift. 120. Plates 20-21 show the tidal current patterns near the inlet for maximum ebb and flood for Plan 1. For clarity, the plotting of velocities below 0.1 fps is suppressed in these figures. These two plates can be com- pared to the base condition patterns of Plates 14-15, but few differences are apparent in a visual examination. For convenience the vector differences between Plan 1 and base condition velocities are shown in Plates 22-23 for the same region near the inlet, for maximum ebb and flood, respectively. Note the change in velocity scale. The plotting of velocity differences below 0.05 fps is suppressed in these figures. Both figures indicate that sealing the south jetty exerts local changes on tidal currents. The large difference vectors at the landward end of the south jetty represent a decrease in velocities between base and Plan 1 since flows in this area are stopped by sealing the jetty. No other significant changes in the current patterns were noted within the study 70 area for Plan 1. The extension of the navigation channel at the seaward end produced almost no effect upon the current patterns. Sediment Transport Testing procedure 121. The testing procedure used was similar to that for base conditions except the computations were performed with Grid 2, and the bathymetry at the start of computations corresponded to Plan 1 conditions. The sediment trans- port model used the results of the tide model for Plan 1 and the results of the wave and wave-induced current models for base conditions. As for the base test, computations were performed for 200 days of prototype time, and the results were used to estimate yearly erosion/deposition rates along the channel. Results 122. The channel was divided into 11 zones for Plan 1 (Figure 23). The exact offshore limit of zone 1A was yet to be determined from field surveys. Figure 27 shows the erosion/deposition rates by zone for Plan 1. A comparison of base and Plan 1 results is plotted in Figure 28. The model predicts an increase in both deposition rates and erosion rates between sta -—9/7+76 and sta 325+00 from base to Plan 1. Zone 1A is not shown in the figure. This zone indicates on the average a slight erosional tendency with rates of the order of 0.1 ft/ year or less. The model predicts deposition in zones 8 and 9 (sta 323402 to sta 374+94) for both base and Plan 1. For Plan 1, the deposi- tion rates are of the order of 1.0 to 1.4 ft/year. Model B predicts large erosion rates in zone 10 (sta 374+94 to sta 399+74). Since there is no quan- titative field information on sedimentation rates in zones 8-10, it is diffi- cult to comment on Model B predictions for this reach. It is suspected that since the bathymetric information used for this channel reach and adjacent areas was not up-to-date, it might have caused deviation of Model B results from field experience. Another contributory factor might be the grain sizes found in this reach, which are much larger than elsewhere in the study area. The model assumes the same grain size distribution throughout the study area. The local deviation of grain sizes might have resulted in the prediction of larger erosion and deposition rates locally. There is reason to believe the effect of these factors is restricted to Model B predictions for zones 8-10 7A EROSION ~+* DEPOSITION RATE, FT/YEAR -50 0 50 100 150 200 250) 300 350) ~ 400 DISTANCE, 100 ft Figure 27. Erosion/deposition rates (ft/year) for Plan 1 condition from Model B (+ = erosion, - = deposition) LEGEND ae ea F BASE ee TAN -530 0 SOP OO SOR 200250 S00 S50 400 DISTANCE, 100 FT Figure 28. Comparison by zones of erosion/deposition rates for base and Plan 1 72 and does not extend to the model results for the rest of the study area. 123. In terms of yearly shoaling volumes, if the reach of channel from sta -80+00 to sta 325+00 is considered, the results translate to approximately 475,000 cu yd/year for base and 788,000 cu yd/year for Plan 1 allowing for the wider Plan 1 channel, or an increase of approximately 66 percent from base to Plan 1. The base volume is of the same order as the maintenance dredging vol- umes recorded in CESAJ dredging logs. 73 PART V: MODELING LIMITATIONS 124. The numerical models used in this study were the most advanced models available at the time the study was undertaken. However, they do have certain limitations which must be kept in mind in order to view the results obtained from this study in proper perspective. As previously indicated, numerical models represent an approximation to the physical processes. The degree of approximation depends on the physics in the formulation of the indi- vidual models, the resolution of the computational grid, and the time-step used in computation. The assumptions made in the models and the limitations of the models have been given previously along with the description of the models in Part II. In this study, the computational grid resolution and the computational time-steps used have been chosen, on the basis of experience and testing, such that the results obtained would be reasonably accurate for engi- neering purposes and, yet, the computational costs would not be prohibitive. 125. Generally, the hydrodynamic models are more exact than the sedi- ment transport model because more insight into the hydrodynamics is available and more experience has been gained in modeling the hydrodynamics numerically. With proper calibration and verification, tidal hydrodynamic models such as WIFM can predict tidal elevations very accurately and tidal currents fairly accurately. Monochromatic wave models such as RCPWAVE are fairly accurate in open coast areas. Their results near structures and inlets are more approxi- mate because of the difficulties and expense in modeling diffraction near structures and wave/current interaction near inlets. As for wave-induced cur- rent models such as CURRENT, people have less experience with them than with tidal and wave models. Wave-induced current models are reasonably validated for open-coast situations. Their results are more approximate near inlets and jetties because the hydrodynamic processes are more complicated and less understood, the wave fields are less accurately known, and there is a lack of field data to validate the models. 126. Sediment transport is the most important aspect of the project for project design; yet the sediment transport model is the least exact of all the models, and the uncertainty is the greatest with this model. The uncertainty exists because sediment transport in general involves complex interactions between the bed and the flow which are not well understood. Of all types of sediment transport, sediment transport near inlets under the combined action 74 of waves and currents, as typified by this study, is one of the most compli- cated and least understood processes. The sediment transport model employed in this study uses fairly simple empirical formulas which are based on labora- tory and field data. It reflects the inaccuracies inherent in the formulas as well as the inaccuracies in the results of the three numerical hydrodynamic models. 127. In this study, a mean tide, and an average year's wave climate based on 20-year averaging of wave statistics were used in running the sedi- ment transport model to estimate the yearly shoaling rates in the navigation channel. In reality, the tidal cycle is more complex, involving spring and neap tides; and the wave climate varies from day to day, season to season, and year to year. Severe storms such as hurricanes, which have a dramatic impact on sediment transport and channel shoaling, have been excluded from this study. As a result, sediment transport and channel shoaling rates in any given year may deviate significantly from the values predicted in this study. Moreover, short-term rates such as averages over a month or a season may dif- fer markedly from average rates over a year. Even the nature of sedimentation at a particular location may change from erosion to deposition and vice versa. This change is exemplified by the field data on shoaling rates shown in Fig- ure 20. Therefore, the results of this study will provide reasonable esti- mates of the long-term yearly average values of sediment transport and channel shoaling rates, provided severe storms are excluded and the uncertainty in the results for the reach of channel between sta 325+00 and sta 399+74 is noted. 128. In general, the uncertainty in the predictions of the sediment transport model is reduced by verifying the model with field data from the project site. For St. Marys Inlet, field data from navigation channel surveys were available for about a year (November 1980 to December 1981) and are free from the effects of extreme storms. The model verification, as shown in Fig- ure 22, is good. In a sense, the verification shown is an indirect verifica- tion of the modeling system approach as a whole. The yearly shoaling volumes predicted by the model for existing conditions are comparable to yearly main- tenance dredging volumes recorded by CESAJ. In general, with proper verifica- tion numerical sediment transport models are better at predicting the effect of a change from one condition to another, such as from base to plan, than at predicting an absolute condition such as base or plan alone. In view of these facts, it is estimated that Model B results on sediment transport are accruate US to within +25 percent for base and Plan 1 conditions. 129. To keep things in perspective, it should be pointed out that at present the only possible alternative to a numerical sediment transport model ‘ls a physical movable-bed hydraulic model. Movable-bed coastal models are fairly complicated and expensive to construct and operate. Such models require more time than a numerical modeling effort. At present, there is no universal agreement on the scaling relations to be used. Movable-bed coastal models involving the combined action of waves and currents near inlets (the type required by the present study) are the most complicated of all coastal models and the least understood. Their results are approximate because there has to be a compromise between scaling relations necessary for waves only and scaling relations required for currents only. According to established ex- perts, the accuracy of a coastal movable bed model of this type in the hands of an expert will be of the order of +50-100 percent. Thus, the results of the numerical modeling system employed in this study are definitely better than the alternative. 76 PART VI: RECOMMENDATIONS Advance Maintenance Dredging 130. The following recommendations on advance maintenance dredging are based not only on Plan 1 results from Model B but also on all other available information such as field surveys and field experience. It must be emphasized that these recommendations are for an average year including normal storms and do not allow for the effects of abnormal storms such as hurricanes and tropi- cal storms. Since the Navy wants a minimum clear depth of 46 ft mlw always and since it plans to dredge the channel only once a year, the deposition rates by zones as well as the deposition rates predicted by Model B for indi- vidual cells (Figure 29) have been taken into account in making these recommendations. 10 LEGEND —— BASE 7 “5 ———PLAN 1 (S] EROSION ~+* DEPOSITION RATE, FT/YEAR (a>) — (=>) 15 -150 -100 -50 0 50 1005 S150 2005 250 3000350 ne 400 DISTANCE, 100 FT Figure 29. Comparison of computed erosion/deposition rates by cells for base and Plan 1 131. For reasons previously mentioned, the high local deposition rates predicted by Model B for base and Plan 1 in some reaches of the channel be- tween sta 325+00 and sta 399+74 are suspect because up-to-date bathymetric data were not available for model calculations and there are no corroborating field data for such high rates. On the other hand, field surveys taken in April 1984 and December 1984 which covered the channel between these stations Ud and which became available after Model B was run, seem to indicate erosion rates of the order of 0.8 ft/year or less between sta 325+57 and sta 361+74 and deposition rates of the order of 1.4 ft/year or less between sta 361+74 and sta 399+74. In view of the uncertainty on sedimentation rates in the length of channel between sta 325+00 and sta 399+74, and because the existing depths in this reach are generally higher than 49 ft mlw, an advance mainte- mance depth of 3 ft is recommended in this reach. 132. For convenience in dredging, the channel was divided into reaches of at least 2,000-ft lengths at the suggestion of CESAJ. Table 5 lists the various reaches of Plan 1 entrance and offshore channels where shoaling is expected, estimates of deposition rates (rounded to 0.1 ft/year), and recommen- dations for advance maintenance depths (rounded generally to whole feet). If the length of channel between sta -97+76 and sta 325+00 is considered and only the rectangular portion of the planned channel cross section is taken, the total dredging volume for advance maintenance in accordance with the recommen- dations shown in Table 5 represents a savings of approximately 630,000 cu yd, or nearly 27 percent, compared to the dredging volume for a channel with 3-ft advance maintenance throughout this reach. 133. The recommendations given in Table 5 do not take into account the long-term economic advantages of providing greater advance maintenance depths and dredging less frequently than once a year, especially in the offshore areas, in view of the high cost of mobilization of dredging plant. This issue should be explored before a final decision is made on advance maintenance depths. 134. From the geologic sections provided by CESAJ, rock seems to be present at depths of 40 to 54 ft mlw between sta 234+00 and 260+00. Two of the reaches where large advance maintenance depths of the order of 7 to 9 ft have been recommended are in this general area. This is the area just outside of the jetty tips and just interior to the jetties. Severe deposition prob- lems have been experienced in this general area at present because of material moving from the shoals on either side of the channel into the channel. Gener- ally, the highest deposition rates have been observed in the northernmost quadrant of the channel. In view of the difficulty and expense of dredging in rock and problems that may be experienced with large overdepth dredging, it is suggested that overwidth dredging be explored as an alternative to overdepth dredging in this area. For instance, in addition to providing a reasonable 78 advance maintenance depth, the channel may be widened by 100 to 125 ft (total width of channel equals 600 to 625 ft) in this reach. Overwidth dredging may be considered also as an alternative in other reaches where rock may be present. Future Testing 135. Model B results for Plan 1 provided in this report have been ob- tained by testing a 500-ft-wide channel with a project depth of 46 ft mlw and advance maintenance depth of 3 ft throughout. Once the channel design is finalized, it is recommended that the final design be tested in Model B with the latest available bathymetry in and around the channel so that maintenance dredging requirements can be determined more accurately corresponding to the final channel design. 136. Model B has been used in this study to estimate average yearly erosion/deposition rates in the entrance and offshore channels under average wave conditions, excluding abnormal storms. These estimates are good for pre- dicting long-term average maintenance dredging requirements. However, the effect of severe storms such as hurricanes and tropical storms on shoaling can be quite dramatic. So it is recommended that shoaling of the planned naviga- tion channel under severe storm conditions be investigated since estimates of shoaling volumes can be used in channel design as well as in advance planning for emergency mobilization of the necessary dredging plant to keep the channel open. This task can be performed using Model B and the storm surge modeling capability of WIFM. 79 PART VII: SUMMARY AND CONCLUSIONS 137. To study the effects of proposed modification of the exterior channels of St. Marys Inlet (the ocean entrance to Kings Bay Naval Submarine Base) on coastal processes, the CIP system of numerical models of CEWES was employed. The system included models for tides, waves, wave-induced currents, and sediment transport. The system together with two computational grids developed for the study was called Model B. 138. Model B was used to study existing (base) conditions as well as planned conditions. Plan 1 is to (a) widen the navigation channel by 100 ft on the north side so the total width becomes 500 ft, (b) deepen the channel to -49 ft mlw (46-ft project depth plus 3-ft advance maintenance) with side slopes of 3H:1V, and (c) extend the channel on the ocean side with a 20-deg bend to the south at sta -97+76. It is assumed also that the landward 1,000 ft of the south jetty is made sand-tight for Plan l. 139. The tidal model was verified using the field data of 10 November 1982. This was achieved by forcing the model with measured tidal elevations and matching observed velocities at ranges in the inlet, Cumberland Sound, and St. Marys River. There was good agreement. 140. The average year's wave climate for the study area was obtained from WESWIS, on the basis of 20-year hindcast data. The data set included normal storms but not hurricanes and tropical storms. This was used in run- ning the wave and wave-induced current models. 141. The sediment transport model determined noncohesive sediment (sand) transport in the study area, under the combined action of tides, waves and wave-induced currents. It considered a mean tide and the average year's wave climate. 142. The sediment transport model was verified by comparing computed erosion/deposition rates in the navigation channel with those obtained from field surveys taken by CESAJ during 1980-81. There was good agreement with respect to both trends and magnitudes. 143. While all four models were run for base conditions, only the tide model and the sediment transport model were run for plan conditions (Plan 1) to meet the urgent need for model results. (Plan conditions were expected to influence the tide and sediment transport much more than the waves and wave-induced currents. ) 80 144. The effects of Plan 1 on tidal currents were mainly local and caused by sand-tightening of the south jetty. Velocities at the end of the jetties and at tide Gage 1 increased by approximately 10 percent. There were no significant changes in velocities at the throat of the inlet, including Range 1 and the Fort Clinch area. 145. Model B predicts an increase in deposition and erosion rates be- tween sta -97+76 and sta 325+00 from base to Plan 1. For the reach of channel between sta -—80+00 and sta 325+00, the predicted yearly shoaling volumes are 475,000 and 788,000 cu yd/year for base and Plan 1, respectively, or an in- crease of 66 percent for Plan 1. 146. On the basis of Model B results and all other available informa- tion, recommendations on advance maintenance dredging were made for different reaches of the navigation channel (Table 5). 147. For the length of channel between sta -97+76 and sta 325+00, if only the rectangular portion of the planned channel cross section is consid- ered, the total dredging volume for advance maintenance in accordance with Model B recommendations represents a savings of approximately 630,000 cu yd or nearly 27 percent compared to the dredging volume for a channel with 3-ft advance maintenance throughout according to Plan 1. 148. In summary, the study successfully accomplished all the study objectives, as set forth in paragraph 3, "Purpose," except for the determina- tion of waves and wave-induced currents under plan conditions. The numerical models for these processes were not rerun, as originally planned, in order to meet the urgent needs of the sponsor. 81 REFERENCES Ackers, P., and White, W. R. 1973. "Sediment Transport: New Approach and Analysis," Journal of the Hydraulics Division, American Society of Civil Engi- neers, Vol 99, No. HY11, pp 2041-2060. Bagnold, R. A. 1963. 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"Modeling Wave Trans- formation in the Surf Zone," Miscellaneous Paper CERC-84-8, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Ebersole, B. A. 1980. "A Numerical Model for Nearshore Circulation Including Convective Accelerations and Lateral Mixing," Master's thesis, University of Delaware, Newark, Delaware. Ebersole, B. A., Cialone, M. A., and Prater, M. D. 1986. "Regional Coastal Processes Numerical Modeling System; Report 1, RCPWAVE--A Linear Wave Propaga- tion Model for Engineering Use," Technical Report CERC-86-4, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Granat, M. A., et al. In preparation. "Hydrodynamic and Sediment Transport Hybrid Modeling of Cumberland Sound and Kings Bay Navigation Channel, Georgia: Verification and Basic Plan Testing," Technical Report HL-88- , US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Hales, L. Z. 1980. "Erosion Control of Scour During Construction; Report 3, Experimental Measurements of Refraction, Diffraction, and Current Patterns Near Jetties," Technical Report HL-80-3, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Horikawa, K., and Kuo, C. T. 1966. “A Study of Wave Transformation Inside Surf Zone,'' Proceedings of the 10th International Conference on Coastal Engi- neering, American Society of Civil Engineers, pp 217-233. Houston, J. R. 1981. "Combined Refraction and Diffraction of Short Waves Using the Finite Element Method," Applied Ocean Research, Vol 3, No. 4, pp 163-170. 82 Jonsson, I. G. 1966. "Wave Boundary Layers and Friction Factors," Proceed- ings, Tenth Coastal Engineering Conference, American Society of Civil Engi- neers, Tokyo, Japan, pp 127-148. Jonsson, I. G., Skovgaard, 0., and Jacobsen, T. S. 1974. "Computation of Longshore Currents," Proceedings, Fourteenth Coastal Engineering Conference, American Society of Civil Engineers, Copenhagen, Denmark, pp 699-714. Komar, P. D. 1977. "Beach Sand Transport: Distribution and Total Drift," Journal of the Waterway, Port, Coastal and Ocean Division, American Society of Civil Engineers, Vol 103, No. WW2, pp 225-239. . 1978. “Relative Quantities of Suspension Versus Bedload Trans- port on Beaches," Journal of Sedimentary Petrology, Vol 48, No. 3, pp 921-932. Leendertse, J. J. 1970. "A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas; Principles of Computation," RM-6230-rc, Vol 1, Rand Corporation. Leenknecht, D. A., Earickson, J. A., and Butler, H. L. 1984. "Numerical Simulation of Oregon Inlet Control Structures' Effects on Storm and Tide Ele- vations in Pamlico Sound," Technical Report CERC-84-2, US Army Engineer Water- ways Experiment Station, Vicksburg, Miss. Longuet-Higgins, M. S. 1970. "Longshore Currents Generated by Obliquely Incident Sea Waves, 1 and 2," Journal of Geophysical Research, Vol 75, No. 33, pp 6778-6789 and pp 6790-6801. Longuet-Higgins, M. S., and Stewart, R. W. 1964. "Radiation Stresses in Water Waves; A Physical Discussion, with Applications,'' Deep-Sea Research, Vol 11, pp 529-562. Parchure, T. M. 1982. "St. Marys Entrance Glossary of Inlets Report #11," Report No. 44, Department of Coastal and Oceanographic Engineering, University of Florida, Gainesville, Fla. Penney, W. G., and Price, A. T. 1952. "The Diffraction Theory of Sea Waves and the Shelter Afforded by Breakwaters," Philosophical Transactions of the Royal Society of London, Vol A244, pp 236-253. Perlin, M., and Dean, R. G. 1983. "A Numerical Model to Simulate Sediment Transport in the Vicinity of Coastal Structures," CERC Miscellaneous Re- port 83-10, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Phillips, 0. M. 1969. The Dynamics of the Upper Ocean, Cambridge University Press, Cambridge, Mass. Reid, R. 0., and Bodine, B. R. 1968. "Numerical Model for Storm Surges in Galveston Bay," Journal, Waterways and Harbors Division, American Society of Civil Engineers, Vol 94, No. WW1, Proceedings Paper 5805, pp 33-57. Sheng, Y. P., Segur, H., and Lewellen, W. S. 1978. "Application of a Spatial Smoothing Scheme to Control Short-Wave Numerical Oscillations," Technical Memorandum No. 78-8, Aeronautical Research Associates of Princeton, Prince- COM, Wa do Shore Protection Manual. 1984. 4th ed., 2 Vols, US Army Engineer Waterways Experiment Station, Coastal Engineering Research Center, US Government Print— ing Office, Washington, DC. 83 Smith, R., and Sprinks, T. 1975. "Scattering of Surface Waves by a Conical Island," Journal of Fluid Mechanics, Vol 72, Part 2, pp 373-384. Swart, D. H. 1974. "Offshore Sediment Transport and Equilibrium Beach Pro- files," Delft Hydraulics Laboratory, Publication No. 131, Delft, The Netherlands. Thornton, E. B. 1970. "Variation of Longshore Current Across the Surf Zone," Proceedings, Twelfth Coastal Engineering Conference, American Society of Civil Engineers, Washington, DC, pp 291-308. - 1972. "Distribution of Sediment Transport Across the Surf Zone," Proceedings, Thirteenth Coastal Engineering Conference, American Society of Civil Engineers, Vancouver, Canada, pp 1049-1068. Thornton, E. B., and Guza, R. T. 1982. "Energy Saturation and Phase Speeds Measured on a Natural Beach," Journal of Geophysical Research, Vol 87, No. C12, pp 9499-9508. Vemulakonda, S. R. 1984. "Erosion Control of Scour During Construction; Re- port 7, CURRENT--A Wave-Induced Current Model," Technical Report HL-80-3, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Vemulakonda, S. R., et al. 1985. "Coastal and Inlet Processes Numerical Modeling System for Oregon Inlet, North Carolina," Technical Report CERC-85-6, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Vreugdenhil, C. B. 1973. "Secondary-Flow Computations," Publication No. 144, Delft Hydraulics Laboratory, The Netherlands. Wanstrath, J. J. 1977. "Nearshore Numerical Storm Surge and Tidal Simula- tion," Technical Report H-77-17, US Army Engineer Waterways Experiment Sta- tion, Vicksburg, Miss. Weare, J. T. 1976. "Instability in Tidal Flow Computational Schemes," Jour- nal, Hydraulics Division, American Society of Civil Engineers, Vol 102, pp 569-580. Weggel, J. R. 1972. "Maximum Breaker Height," Journal of the Waterways, Har- bors, and Coastal Engineering Division, Vol 78, No. WW4, pp 529-548. Williams, R. G., Darbyshire, J., and Holmes, P. 1980. "Wave Refraction and Diffraction in a Caustic Region: A Numerical Solution and Experimental Vali- dation," Proceedings of the Institution of Civil Engineering, Vol 69, Part 2, pp 635-649. 84 BIBLIOGRAPHY Florida Coastal Engineers. 1976. "Beach Erosion Control Study, Nassau County, Florida. Appendix 2." Report prepared under Contract No. DACW17-75C- 0039 for US Army Engineer District, Jacksonville, Florida. Jensen, R. E. 1983. "Atlantic Coast Hindcast, Shallow-Water, Significant Wave Information," WIS Report 9, US Army Engineer Waterways Experiment Sta- tion, Vicksburg, Miss. Olsen, E. J. 1977. "A Study of the Effects of Inlet Stabilization at St. Marys Entrance, Florida," Proceedings of the Coastal Sediments '77 Con- ference, American Society of Civil Engineers, pp 311-329. US Army Engineer District, Jacksonville. 1984 (revised March 1985). '"Feasi- bility Report with EIS for Beach Erosion Control, Nassau County, Florida (Amelia Island) ," Jacksonville, Fla. . 1984. "Fort Clinch, Nassau County, Florida," Section 103 De- tailed Project Report and Environmental Assessment, Jacksonville, Fla. Vemulakonda, S. R., and Scheffner, N. W. 1987. "Application of CIP Modeling System to St. Marys Inlet, Florida," Proceedings of the Coastal Sediments '87 Conference, American Society of Civil Engineers, Vol I, pp 616-631. 85 Table 1 Numerical Gages Used in WIFM Numerd caliGageinOe spe ay ete ti men Ly MCCA Sem aries een aan 1 Prototype tide Gage 1 (south spit) 5 Endeco velocity Gage 2 (main channel) 10 Range survey Gage 1-A iil Range survey Gage 1-B 2, Range survey Gage 1-C 25 Ocean end of jetties—channel Bi Fort Clinch 28 South channel (Amelia Island) 29 Channel to Cumberland Table 2 Sample of WESWIS Data for St. Marys Inlet 69.9 60.0 - CH_ANGLE(DEGREES) Hi TOTAL LONGER 11.0- 9.0- 10.0- 9.9 10.9 F HEIGHT AND PERIOD BY DIRECTION PERIOD( SECONDS ) HEIGHT( METRES ) WDRASCNMSSOCSO At ann Tene rir o eee ree er eee BS MOC > © & © © oe oD a ] Cx) a) +r LALA ord 2 6 6 © © ot) wu o PUAN oro 6 © ot Ca] i OUNTOTFAr © 6 6 ot ron mmr N °o SMAOMO 2 + * +O On aN +r N rm © NO 6 6 0 © 0 © og) mor Nu Cy) na] OF 6 6 0 6 0 6 6 o> oo nR Ds) mm (va) V9 CC CY = 9 wh a sro wy CUM) 6 6 6 0 eo 0 oo ot ao + Tt is4 Ww = DADAAAHAAO SL SS NAN CORES) OD0000000 0 Of COCCCOSOCOCOF- Nonomonone Ooo 010 0 000 0 COmANNMMS TiN TOTAL 79.9 11.0- -9 LONGER 3.2 70.0 - -0- 10 10 ANGLE CLASS Z = OACH_ANGLE( DEGREES) 3.45 F HEIGHT AND PERIOD BY DIRECTION PERIOD( SECONDS} LARGEST HS(M) 0.69 AVERAGE HS(M) HEIGHT(METRES) ATFOOTFTFNCSCOO ORSINED «© 6 6 6 ood Room ca) on pa MoMA AeMMME Aine 536 AnnormM ml wot 270 el HHO 6 6 0 0 0 8 oe Oo Ss} fea salealcalcatcalcalsalcalcad- ¢ SEATS ESI Ce Oiala lati DEO COAT Dene Oh Ooocococoocoor- MoOMNoMnonona oe eee eee eee SORANANMMESIN TOTAL 89.9 SB Goal 80.0 - 11.0- 9.9 10.9 LONGER 9.0- 10.0- “OMMOLAD ANGLE CLASS Z% OACH_ANGLE(DEGREES ) ZIMUTH F HEIGHT AND PERIOD BY DIRECTION 3.28 PERIOD( SECONDS )} LARGEST HS(M) 0.62 AVERAGE HS(M) HEIGHT( METRES) ABDODOMAONUHOOS FAUMOMAM ort «> MONASH rion Ln Ua | 313 3310 2395 AAAAANOR + « SnOkNNA De aa) ric OLOMSAe NoOMnmMr ° ° ° i NMOMRN Linc 1491 ANGLE CLASS Z AAMNCor~ WO tonor oor Cal 2 0 é 3 0 747 1746 4.32 wy © COTM © © 6 6 © og + na) LGD © © 6 © 6 © © oh oO N CeCe CCT: «) r AAADAAAAGKAO ST SSS OO OOOO OO Od SO IOS SOT PSO DSU ED UUs US Tes ooooocoocoooF NOMNoOMoMNoMNo OO OO OONONO nO 0 SORANNMMIS SW 12.6 LARGEST HS(M) 0.72 AVERAGE HS(M) Table 3 Incident Wave Conditions for St. Marys Inlet DERE EIEN DEES) HEIGST (FT) PERIOD (SECS) FESCENT CUM. FRED. OCCUR. 2. ei 2 043 1 -? 22 3.20 4.31 0434 2 -72.50 2.26 5.39 1,917 06228 3 -72,50 4.40 6.30 235 18463 4 -62.5 82 2.50 2.102 OSE65 5 -52.50 2.46 4.5 £1233 “09793 i -62.50 4.10 6.20 58 30378 ? -62.50 5.74 7.09 220 30538 8 -32.50 132 2.40 $1853 32864 9 -22.50 2.46 4°70 11315 13776 10 =59159 4:10 5:70 404 141g it -=2,50 5.74 5.80 132 gai2 12 -£2.50 7.38 7.40 1032 14404 13 -43/59 182 5120 2.733 117202 14 ~£2,50 2.46 5.50 1.635 19897 15 -42,50 4.10 5.79 444 19344 16 -£2,59 5.74 6.20 116 119457 17 -62,50 7.33 2.20 1 13572 18 -32.59 22 7.20 9.409 263981 19 -22, 2.48 5.30 11235 30376 20 -32,50 4,10 6.00 1456 30232 2. ~52,50 5.24 6.69 iSES 30987 22 -32,59 7.38 7.20 029 131077 23 -22.50 122 4.39 11415 32433 24 -22.50 2.45 4.90 11443 122641 25 -23150 4:10 5.60 377 34013 26 -22.50 5.74 6.50 823 134147 2? -22.59 7.33 7.30 124 24263 23 ~12.50 182 2.00 2.585 137783 29 -12,50 2.45 7.90 2.574 40157 30 -12.59 4:10 6.60 “656 140813 ai “12.50 5.74 2.00 259 41072 3 -12159 7.33 7.50 134 41206 3 -13150 3182 7.40 $99 41305 34 -2.5 32 8.50 5.249 46554 35 -2.50 2146 2.50 4.909 151453 35 -2.50 4:10 3.30 1.349 152912 37 -2.50 5.74 8.00 ‘546 53353 33 -2,50 7.38 2.80 233 133646 33 -2150 9.02 3.30 193 153839 2 -2.50 19.66 3.70 06! 753300 43 7.50 122 2:10 4.197 13097 49 7.50 2,46 6.70 2.5 60629 43 7.50 4.40 6.90 1.075 61704 44 7.50 5.74 2.43 1439 162193 45 7.59 7.33 2,30 132? 162520 46 7.50 9,02 7.69 178 62693 47 7.59 10.66 2.50 065 $2763 43 17.50 182 6.00 2.792 165555 43 17.50 2.46 5.40 1.502 67057 50 17.59 4.10 6.00 761 ‘67818 51 785 3.74 6.60 1327 68145 52 17.5 7.23 7.90 1238 52263 53 17.50 9.02 7.59 153 852i 54 17.59 10.66 7.59 118 69639 55 27.50 132 4.40 1.177 162316 5 27.50 2.46 4,20 1.164 £20380 5 27.59 4,19 5.39 616 75595 53 27.50 3.74 6.20 370 178366 53 27.59 7.38 6.90 25 172220 60 27.30 9:02 7.40 208 72428 61 27.50 10.66 7.50 155 172593 62 37:50 182 2.69 73321 63 37.50 2.46 4.20 11244 174565 64 37.5 4.30 5.30 6 75474 63 37.50 5.74 6.20 1498 175969 65 37.50 7.33 6.90 306 28275 67 37.50 9.02 7.59 149 176424 63 37.50 10.66 7.50 068 76432 63 47.50 82 2:70 997 77383 70 47.50 2.46 4.40 1.225 ‘75614 2 47.50 4.10 5.40 1.088 29202 72 47.50 5.74 6.00 434 3012 73 47.50 7.33 6.70 031 ‘80227 24 57.59 182 4.10 1.706 81933 25 57.50 2.46 5.20 2.106 64039 76 57.50 4.10 5.70 1939 184878 77 57.50 5.74 6.10 070 184948 23 67.59 22 4.90 4.051 22399 ? 67.50 2.46 5.79 ‘624 123693 80 ‘00 00 100 «= 10.317 100800 Table 4 Details of CESAJ Examination Surveys Sue a nLiclustvclDatessaa ln lll ml NiSUrveyedlistattons 1 21-25 Nov 80 130+00 to 325+00 2 8-9 Dec 80 -80+00 to 130+00 3 31 Mar-13 Apr 81 130+00 to 325+00 4 13 Mar-13 Apr 81 -80+00 to 130+00 5 8 Jun 81 130+00 to 325+00 6 8-10 Jun 81 -80+00 to 130+00 7 14-18 Dec 81 -80+00 to 325+00 Reach Table 5 Recommendations for Advance Maintenance Depths of Channel (CESAJ sta) -97+76 42+38 128+72 181+20 225479 249+03 276+31 325+00 to to to to to to to to 424+38 128+72 181+20 225+79 249+03 269+85 310+38 399+74 Estimated Maximum Local Deposition Rate ft/year 0.3 0.3 1.8 3od 6.9 8.2 1.5 Recommended Advance Maintenance Depth ft 1.0 1.0 2.0 4.0 7.0 8.5 2.0 3.0 ll | ii il ll ll i MMi TOT ATTA OAT ey eee CATA UU a te SET UPTO CLT Ht \ \ | aL itt lil lll il ll I Il FEEREes ILL Au i CT SEATTLE UT TSW 14 ‘NOILBAIT3 DAY OF THE MONTH OBSERVED TIDAL ELEVATIONS 1962 NOVEMBER ST MARYS ENTRANCE, SOUTH JETTY PLATE 1 SGA]a YITINE *HObIG YNIGNUNASS CBb1 aAaGWIAON SNOILYAS74 TWWO1L GsAdaS80 HLNOW 3H1 40 AQ ee be Comme m™m Cc m™ <= D — S) = ral — =< ep) [c~ PLATE 2 ¥900 3IIANIS Ak¥d TNOTLYN “A3ATS SAdbW 1S c8bl aAAEGWaAON SNOILYAI13S WOTL GaAa4S80 HINOW 3HL 40 Abd Ce fen oe te Bs OU zl A Ih TSW 14 ‘NOTLBAR13 PLATE 3 LI IT Il Alle Hie UA A uy 1982 UU CUMBERLAND SCUND INA CUO TCUTUTLD TTT NT AU AL OBSERVED TIDAL ELEVATIONS IM HTN INA ae Bee DAY OF THE MONTH Mt ae BEE aL SATE ny Ee Poe HEMT Sas CO UI | WET | | CN TSW 14 ‘NOI18A3713 PLATE 4 SULT HA at UU e2 = “~ ' WIWSETEHOZ UF TODA GAGE 4 (CUMBERLAND SOUND) iL Pee LETTS Bane ~~ fu iy] et tt peau PEPE PROTOTYPE TIDE GAGE 3 (ST MARYS RIVER) LN LOT LITE LULL TIRE, HOURS TIRE, HOURS é c 2 : | 4 & oS s W iw : = ' : | & z e E MEE’ SeH’AGY ON°SEO°ON’b-oUd¥E 11532 BNNIS Sd4 3° 8@10HS3YHL YOLIIN Sdj °@3 <———_ 831095 YOLIIN SUH °9 83WIL NOTLYINUIS $¥Y0L93M ALIIOIIN 1300u Ob °XUWH Ten TUN PLATE 6 SS°X¥WH LIINI SAYUYH LS °S3D¥9 HdYYIONGAN TWOTYSWNN SNOILY901 3909 ALIO013N 13008 oe ° eocccoeeed 8eNIWH Or=XUHN STeNIWA PLATE 7 2870T/T3 - S30IL (HSYG) NYBW AdALOLOYd SNM (AI10S) IWOTYSWNN SYUNOH “SWIL SUNOH “3WIL A a LW) a : ae : L BSA ss 2 i 2a 4 N Bea or 4 2a 0 L pr L v ee Sa ane 3 P| aon 4 Sas5 a 3 3 NU1N3GWND) % 39V9 SGIL 3dALOLONd ~~~ ~~ (Y3AIY SANYW 1S) E 39¥D 3GIL SdALOLONd ~~~ ~~ CONNOS GNCINNOS ONVIMaauNO) 6 3909 30TL CY3nTa SAMv 1S) E 39¥9 3GIL SUNOH ‘BIL SUNOH “SWIL a a n fn b) h) N N L a F 4 N N 0 0 I I 1 L ; ; n 3 3 1 1 3 3 3WY) 2 39V9 3CIL 3dALOLOND ~~ ~~~ (A3INI JO ALL|P HLNOS) TF 3DVD BGIL _3dALOLONd ~~ ~~~ CUSATS OT eAIe UT auu) 2 3500 Sard” (43 1NI JO ALL3e HLNOS) TF 399 30I4 PLATE 8 €2870T7TT) SIILIDOI3N (HS¥A) AdALOLOYd SN (UIIOS) 1¥3O1Y3KNN SSNOH “3WIL ey 91 st LAS Et ev 123 ot 6 SUNOH ‘BWIL el et 1 oF 6 8 e Bt 2t 9 St of aes H 1 @2t- y 0 Wi CEP Ty 0 u e 3 s eo 3 3 5 eet 3 a est SUNOH “SWIL S 3 Z 3 a n 1 I N 5 ¥ W 9 0 1 3 A JIVINNS-ET SONYA 3dALOLONd HLd3ddIW-at SONYY SdALOLONd ~~ d-T 3909 AANYNS JONYA (RES t Ss SUNOH “3WIL dt ot st ot et ev 125 t:) BdVANNS-YT ZONVY 3dALOLOYNd Hid3ddIW-¥t SONYA 3dALOLOYd ¥-T 3999 AININS JONVA F Dee Sa (a ee (xee a a aS a eS 2 eS SSS ies [is Fi Fema noe | oe > el] ees eel |e Get est QwWoewwWwn UwG@ok FOtest PWHOO ECUZ—F-DOW LAW RANGE SURVEY GAGES 3-ABC PROTOTYPE RANGE 3A-MIDDEPTH PROTOTYPE RANGE 3A-SURFACE RANGE SURVEY GA' PROTOTYPE RANGE PROTOTYPE RANGE PLATE Ww ih Y) e ° ° ° ° ° ° nwresrtesmnanwwe aw aw ° PwWwAI0GO ECUZHEIAW LAW wn 7 8. Ww w Ww ° ° e 5 ° ° ° ° . WwW wwrTrr ma mM YW HW we ow ° 2SWIAIOU ECUZe-DAW LuANM ii ie 13 14 1S 16 17 18 TIRE, HOURS 10 TIME, HOURS a ® TIAE, HOURS TIME, HOURS NUMERICAL (SOLID) US PROTOTYPE (DASH) VELOCITIES (11710782) (287OE7ET) S3BILID01ISN (HSYG) 3dALOLOYd SA (GI10S) WOTYAWNN SHNOH “3WIL SUNOH “3WIL H i a fo) WN i ie) a 4 Ss 3 3 a 3) | cc SUNOH “SWIL SBNOH “3WIL st vt es et 125 et 6 8 é °@ SiS pia Si ee PUAOO E£COFHrIAW LAN Hicsdd THe aONvH adatotosd HLd3ddIW-8E JONYY 3dALOLOSd Jav-E $3909 ABNENS JONYY da¥-E S39¥9 ABNYNS JONVY auoeuwwH Leo FZoerst PWAOO ECOTHEDAW LAM PLATE 11 (287037bE) SAILIIOIZN CHSYG) 3dALOLOYd SN (AIT0S) IWITYSWNN SYHNOH “3HIL H 4 e. (9) N wu (0) C. 3 Ss 3 3 a 9 3 qa SYNOH “SHIL SUNOH “3WIL et et 2SuUAI0O0 ECOZHFEIDAW UW JIVIUNS-Ab BONYVA 3dALOLONd 39¥3yNS-Yy FONVA 3dALOLOYd Hid3dqdIW-&) 39N¥Y J3dALOLOdd HLd3S0dIW-¥y 39N¥A JdALOLOSdd Sa¥-% S39¥D AANUNS 3ONYHY = ——__ 98¥—-— S3IDN¥D ABAYNS FIONA AWOAaWWH LYOEF ZOkrFT SWHOO ECOZH-DAW uaANn PLATE 12 -~ u 0 SN e@ «a » =~ =~ ww Ww Ww i) - ~ 3 pa) WwW =) a : fo) & f=} & $ A a = =) R w J < (5) i) a 5 URUEY GAGES 4-ABC EROTOTYPE RANGE 4C-MIDDEPTH PROTOTYPE RANGE 4C-SURFACE TIRE, HOURS ° ° ° ° ° ° ° pwrewremnaw we ae PWHAOCO ECUZHEFIDIAW UdW QuoeewWwHW LeOr ZOerrT PLATE 13 anthtat ARAAA AAA ADPPPIPPP Pan paanan att ttt tht haanaaanan met trtt ht hasaaaaan matt rt tt harasaaan oi FPS be, | vangane a qv va el VAgeazans ‘4 thi anaaraa V4 Ttanaarxo V4 URC Roxas ‘nt \ \ lO gone VECTOR SCALE: ——————> 10. FPS > ewvewwywvw 9 vwvvwvawey Yvwvwwwea Vvuvwv wa a 4 vvv + 42 32 2 2 dD oD SIMULATION TIME: 7. HRS VECTOR THRESHOLD: AIS VY bo SS Hb oe DV OV RO VY & © & © Ses) Ses po eteile 5 cea) Ge ae 9 SP OO EP Ey ere > ED SS e514 49199 7 a A A ee edd Si->. E Dd SS DS AS Pe Pe Pe ee > MODEL VELOCITY VECTORS eae aes aS aes Yon See cs Lop Sea Suey Jae DS Yuet yy et Seeet te Jy me eee OU SRC TG Siete Sine Yea’ aires Yee ame ae Suen Skee kee Sere Sant Samer Your Yama Slat Yee Yoet Yee Year et Yuk Yue g 9 ae Sh oe} Q 4 A a a a a A a a a a 4 a 4 4 a a 4 4 4 4 4 = 5 ' VELOCITY FIELD AT MAXIMUM EBB - 11710782 ‘Nb Oo Db wv > a ip 7? K oH Reeprrve > 7 /, Mawr ee ey “GODARD ea =~ Edi TAPE PEP ROOD. 2 SS BP LVI ILILER POOR B004 6 BS a PONV LTR GoOOGAOR as 7 BLA PYLE PERRO] A2Q0OL >> rs 2d Vv SSS SS SS “SY HAIN=8 UMIN=12 PLATE 14 2 Sy a EY x x ~ x Br) a = ~ ~ > > > > = > x > > > > > ~~» > > > > > > > > 2878b/TE — d0014 WNWIX¥H LY d13I3 ALI9013N Sdj $° :Q@1OHS3YHL YOLI3N Sd3 °@t <——— 231995 Y0LI3N SUH °yt t3WIL NOILYINWIS S¥O0L93N ALID013N 1300 v v v v 4 » a re ate ¢ re ¢ viv > vvv ? eee eeee bY | ee oan o & eewe«x «& ns byneua & & bey vw Keke Kw Ke & wae ¥¢ ee & b& & OOO O~ a2 00° Jlliéverr \ y y \ \ \ ! : { f J Ll lbdddecever \ \ \ \ \ \ \ | \ | \ \ i i a a ee Ee > > > > 2 2S VWITSFAN\ RULER POO V POO CSS SG V> AP AddY eee eee Vhovby lie V7 Td hal Oh Mis eeees B.C. C b vy » > > > > Wn, vy Vv Jif IV IV dil GUE Oe ries Beh COLA Ge EE v <_ € < a CH MOG GB COO BCOOTS ae <_ 8=NIWH PLATE 15 lacs eee ECON ELEM nae Uh CBE (SOUTH SPIT) 1 (SOUTH SPIT) a Et a TITS PLATE 16 1@ 11 i@ 13 «14 1S 16 17 8 18'! | TIME, HOURS errr ccoL POU CoR Coe Han AMBER Gab SUAMU EOE TIME, HOURS NUPERICAL TIDAL CURRENTS: BASE (SOLID) VS PLAN 1 (DASH) nan ° ° e e e e ° e e Tr anmnnwm Uw we we 2 @ 2WAIOG6 ECOUZHFrIAW LAN NUMERICAL TIDAL CURRENTS! BASE (SOLID) US PLAN 1 (DASH) up CRRRERSARAIL BCC SLI eCCOUCDLerT TIRE, HOURS PLATE 17 EH SIR ae aes OSE HUE OG Aa UCC TON Ae Hemmings JOE REIEGT OCP CC LETT, TEEPE eae ae PEE PP S-CHANNE L 12 te 13 14 is 16 1? 18 TIRE, HOURS JETTI Eeeconnel JETTI TIRE, HOURS 9 10 it 12 13 14 is 16 17 18 a = NUMERICAL TIDAL CURRENTS: BASE (SOLID) VS PLAN 1 (DASH) TIME, HOURS TIME, HOURS CE PCL CO SOUGROetnO 10 ii ie 13 14 1s 16 17 18 8 10 11 12 13 14 1S 16 17 18 RANGE SURVEY GAGE 1-C -. RANGE SURVEY GAGE 1-C Ebel el sea ae cee ze a\ ze PEE EN eee [ae a (a a A a Fe (os ee PLATE 18 : : 8 : : s 2 l 2 oe |e) eS a Oe (ee ee a ee ° e ° ° e ° ° ° ° w rr ana nm MN MN BA w= e SudOO ECUZHRIAW LAW AauUVGeWwwWwH LeOL LOerTE PEATE U9 NYTd 2883 WNUIXYW LY G1IZI4 ALIIO13N Sdj f° :Q@10HS3YHL YOLISN Sdj °@. <———_ 231995 40L93N SUH °2 s3W1L NOTLYINIS SYOLDIN ALIIOIIN 1300W Ob- XOWh 4 4 7 a 9 a @ qv v v 2 7 > >? v v v » > a Rilaaa dD > *jza0de1 YW TepoW 9es >>»? > ¥ kaa aan tans Ssq[Nset AOFASRUT A0F s9ION PRD? vd iy [7 RDDD> DP D PY be 4la ad D dD ala aa dD > RPP? D> d wey CAAA RH tt? tt tts tts tt ’ . FAAAR RAR RR F 4 AAAAA ARAB A Daa » @ #9 lSiaauete aes » @ SS & GAA IS MEEK i ek el i Sa St Sy Sey Sey SL weebeoe bBo eS ry LJ ® & & ® & & &® & g ® SS _— ~— — e + = -_— < ¢ ¢ ¢ & i} & & i & x g ® A 3 wn ~— ~ - + ~~ «< <— e <¢ + ¢ ¢+ ¢ ek&eabhehehb e@ee¢e逢¢aéa 4 4 4 re & SS°XUMH Bulan eeNTbn PLATE 20 ¥ NUId 300014 UNWIXYW LY G13I4 AL19073N Sdj T° 3:0 10HS3YHL YOLIIN Sdd °OS <——__ 231¥9S YOLITA SUH °rt s3WIL NOILYINUIS $YO0LI3A ALIS013N 13d0u » » b *310de1 VY Tepoy ses S][Nsel AOTA9UT 10g +:970N 6 6 b&b & & & & & a weee ea & wmeead © becceseee Bo b> » bbe eosee ob © Ray H vekekeae b ry sé keeev &B EL yeeeeeeeee bw GECCGGOC OG © bids a Hubesey dye bysees | | a . a . a s 7 = =a a ~ ~~ ~~» >» > — =» —> > > > > Hee Leeee aS way vv ve SS°xXvuH etentun PLATE 21 HAAX2SS HAINSS UNIN= te PLATE 22 ? > DP PL - P O. Fi DD, DD. Fo VE Ve 3. 7 v7 >>ds dB 3d 2 2 >> rrrrry > - a a a a > b +s 3B aaa. J 77}VP Hdd 3 > 4 ‘a77>> 1 It riyyra> >eres TVPPR-AAAA : TUNPPdAAIAS IIMdayydd atatiauyyy Aaanirtl PII ¥ Ce > ny AAAAD ALY he, hee vv Se RES v FESR Ve rre. FPS SIMULATION TIME: 7. -@5 FPS VECTOR THRESHOLD: - BASE PLAN 1 CURRENT DIFFERENCES, EBB TIDE: 2€:iedeigin rbereds HMAX=SS FPS ' eepadceece ; Laneeree HRS VECTOR SCALE: ——————>2. -05 FPS oT CS eee Set Sent Seer Say Sy bee vbevbiak & om een vvvvs ie ta = geoces ee eee | SIMULATION TIME? 14. VECTOR THRESHOLD: & &e&ee_ei kei sea vip ¢€ ev @aid 3 3 vervvvvvas © efi dd ¢ ee eue € Ww or °o & oO Ww > > (Ss ~ Oo i=) CI uw > ) tw a i=) Lg FLOOD TIDES CURRENT DIFFERENCES, PLAN 1 - BASE lts see Model A report. : For interior resu Note VATNele VAIAX= 4@ PLATE 23 al J a pn APPENDIX A: NOTATION Wave amplitude function Ratio of volume of solids to total volume of sediment =l-p Mapping constants for region p in x-direction Mapping constants for region q in y-direction Area of cell Drag coefficient, wave celerity Coefficient Wave group velocity Chezy coefficient Local total water depth Sediment diameter exceeded in size by 65 percent (by weight) of sediment sample, energy dissipation term Wave energy density = peH-/8 Coriolis parameter, drag coefficient Terms representing external forces Wave friction factor with D as bed roughness Acceleration due to gravity Local still-water depth Wave height Wave height in deep water Unit vectors in the x- and y-directions Local immersed weight longshore transport rate Total immersed weight longshore transport rate Number of water cells within the surf zone Wave number Empirical coefficient Empirical coefficient Bottom slope Maximum values of cell indices for RCPWAVE Ratio of group velocity to wave celerity = c /c , Manning's roughness o Porosity of sediment Local volumetric sediment transport rate due to currents Al Local volumetric sediment transport rate Local volumetric sediment transport rates in x- and y-directions Rate of water volume change due to rainfall or evaporation Arbitrary variable, mass density of sediment relative to that of fluid (specific gravity of sediment), wave phase function Radiation stresses Time Wave period Wave orbital velocity at the bottom Time average of the absolute value of the wave orbital velocity at bottom Tidal velocity components Velocity components due to wave-induced currents Total velocity component = u + U Shear (friction) velocity Longshore velocity Total velocity component =v +V Coordinates in real space Width of surf zone Dimensionless grain diameter Coordinates in computational space Breaking index = H/h Proportionality coefficient Centered difference operators Time-step Cell dimensions in real space Cell dimensions in computational space Eddy viscosity for tidal model Eddy viscosities in x- and y-directions Bed elevation Tidal elevation above datum Mean free surface displacement (setup) Hydrostatic water elevation due to atmospheric pressure differences Angle of wave propagation Wave direction in deep water A2 6 Contour angle : Rate of energy dissipation coefficient kK Refraction coefficient Se Shoaling coefficient Ue» n Grid expansion coefficients v Kinematic viscosity of fluid T 3.14159... 9) Mass density of sea water D . Mass density of solids fo) Wave angular frequency = 21/T cA Bed shear stress eee bes, Bottom friction stresses in x- and y-directions toed Lateral shear stress due to turbulent mixing > Complex velocity potential for wave Superscripts k-1 Previous time level k Present time level k+1 Next time level x Intermediate time level Subscripts b At breaking s Stable level of a variable ft Partial derivative with respect to time A3 yes ‘hbaicheny wes Pe ee. F eas (apedt jo panna bit ie | aie thn ie ie ee oe pied - i if an - ie aenient' se . oe nod Pan Tinie SVORn Qe he , nae ae tt agentes me Donn es se iv ee ; eae’ i. ‘a Fa ml : nD 7 he ZZ Bhad Ais deedagh ‘eghantis ‘ 1g) airlines, tre aun eunes | am Potent, eat inbty: ‘Hoven canient fai mk anand fey Ggondiion hth ha, env pyar ioral md “Sholk om SRR oF enue aietig Liew X: et oe Rie (Ota athe iW Ail ioe (9 : a 10 eet take te BUEN Kin: | oe a ah, ae ay mat hag eye be 1 0 4404 faved a\ dase hi a “Wp Om Brennen iy inva ral Tanah me 7 a Bein et het ill ety efuned apart yes a ai itm erp i haa y Cane teeny Lane ve Wid wine | i, ' i ia | eh at f i “i Veta { ns fonr at an ne en | 4 aay ident hey Mang: Weal ake i oe , rae WORT eC Mt ee ee ee (haat Ge ene ein ; eer a tenee atone tun’ abet ha ee | eanaw Lenny era AOR) abel Caaenii! ; abso a MONE davattonin' 18, vowed. wren - Me Levebrnm m a ici, Sn | i ei be wee, Ww pert pays ‘a. TT alates é ay ll Ban i, iT ad obi sven ‘oe a iH i m i il Mt a a ny aa WW iy a mlw msl mwl NGVD NOS OICC RCPWAVE SC swl USGS WESWIS WIFM APPENDIX B: ABBREVIATIONS AND ACRONYMS alternating-direction-implicit Coastal Engineering Research Center US Army Engineer District, Jacksonville US Army Engineer Waterways Experiment Station Coastal and Inlet Processes Hydraulics Laboratory mean low water mean sea level mean water level National Geodetic Vertical Datum National Ocean Service Officer In Charge of Construction Regional Coastal Processes Wave Propagation Model stabilizing-correction still-water level United States Geological Survey WES Wave Information Study WES Implicit Flooding Model Bl nee t mee ory Lt 52 ef eee Oe ey Ts o mrss le t : Ls ‘ 1 ary i “—*, Core tae i UA SEAT CF Viet lea 4 ‘ " ¢ 2 ayer Tray Ae Geko aA is Oi pee a wee er b . ie ity n a) \hor ‘ s f mh aT ti { : , vi H f rsa ayiny emo J ‘ hs j 7) rT ay AV AWTS 9 he Yow ' rt ye , 7 ‘ ‘i r at y ‘ i . t ‘ New i i i q : | i Re a itt i = ' 1 my od? i Ay) x a i t i i ‘ HT j b ' i n en i Y i Oat vt vet i i teu i t ¥ : 1o 7 : if r \ 7 y i j \ 1 i 4 i \ Sen aye pedal ely © caeat pe te