UL, Avwug Coal, oa Kes Gz TP 78-1 Wave Transformation at Isolated Vertical Piles in Shallow Water by Robert J. Hallermeier and Robert E. Ray TECHNICAL PAPER NO. 78-1 MARCH 1978 DOCUMENT | Niele: | Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING oa RESEARCH CENTER | (50 Kingman Building | ac, Fort Belvoir, Va. 22060 no 7 - | Reprint or republication of any of this material shall give appropriate crédit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 22151 Contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not const’ ‘e use of such com T as an official De; ed by other autl bDEMCO ANNA 0 0301 0089981 1 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) | READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO,| 3. RECIPIENT'S CATALOG NUMBER TP 78-1 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED WAVE TRANSFORMATION AT ISOLATED VERTICAL PILES Technical Paper IN SHALLOW WATER 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER(s) 7. AUTHOR(s) Robert J. Hallermeier Robert E. Ray 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of the Army Coastal Engineering Research Center (CERRE-CP) Kingman Building, Fort Belvoir, Virginia 22060 CONTROLLING OFFICE NAME AND ADDRESS Department of the Army Coastal Engineering Research Center Kingman Building, Fort Belvoir, Virginia 22060 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS A31222 12. REPORT DATE March 1978 13. NUMBER OF PAGES 187 15. SECURITY CLASS. (of thia report) 11. UNCLASSIFIED 1Sa. DECLASSIFICATION/ DOWNGRADING SCHEDULE Approved for public release, distribution unlimited. 16. DISTRIBUTION STATEMENT (of this Report) 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse aida if necessary and identify by block number) Channeled piles Wave direction gage Circular piles Wave forces Surface effects Wave runup Velocity head Wave transformation ABSTRACT (Cantinue em reverse side if neceaesary and identify by block number) Water level was measured within the flanges of a channeled pile, or near the surface of a circular pile, for isolated piles in a periodic wave train. Measurements are plotted as 160 patterns of crest height versus orientation with respect to wave direction. All patterns have a maximum at the front, facing into the wave, and a lesser maximum at the rear. Intervening minimums are symmetrically located at the sides of the pattern, usually slightly toward the rear. As wave height increases, the front maximum becomes higher, (continued) DD ian, 1473 — EprTion oF 1 Nov 65 1s OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) 20. SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) depending on calculated velocity head. The angular width of the front maximum depends on channel geometry of the pile, tending to be very broad for a pile without channels and narrow for a pile with deep channels. With H-piles having deep channels, the pattern minimums occur farther forward than with unchanneled piles. Geometrically similar piles of different size result in similar patterns. The patterns for finned and smooth circular piles are similar, except that the finned pile results in slightly higher and narrower front and rear maximums. Applications of the reported conclusions to the design of nearshore pile- Supported structures are briefly discussed. Twelve different vertical piles were tested, including circular, circular with radial fins, and various H-sections. Pile cross section and water depth were small compared to wavelength, corresponding to typical nearshare Situations. Electrical gage records and photos show complicated surface effects occur near the piles. Crest stagnation can be similar at circular and channeled piles with three stagnation regimes: smooth, breaking, and jetting runup. Smooth runup occurred in most tests, with a nonbreaking bow wave formed at the front of the pile during peak forward flow. 2 UNCLASSIFIED eS SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREFACE This report is published to assist coastal engineers and scientists dealing with wave action at pile-supported structures by providing re- sults from a laboratory study of wave transformation at a variety of vertical piles. The tests were conducted at the U.S. Army Coastal Engineering Research Center (CERC) during an effort to develop a near- shore wave direction gage utilizing wave transformation at a surface- piercing pile. The study was carried out under the wave dynamics program of CERC. The report was prepared by Robert J. Hallermeier, Oceanographer, Coastal Processes Branch, with assistance by Robert E. Ray, Civil Engineer, Coastal Design Criteria Branch. Dr. Hallermeier worked under the general supervision of Dr. C.J. Galvin, Jr., Chief, Coastal Processes Branch, who initiated the study. The tests were performed by J.C. Jones, R.J. Karlitskie, R.E. Ray, and C.R. Schweppe, with continuing assistance by R.P. Stafford. J.C. Ahlquist, D.C. Fresch, B.H. Gwinnup, L.B. Keely, C.F. Thomas, and S.B. Ward assisted with the data reduction and display, and J.T. Dayton assisted with the photography. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. JOHN H. COUSINS Colonel, Corps of Engineers Commander and Director CONTENTS CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI). SYMBOLS AND DEFINITIONS. I INTRODUCTION . 7 é lee Contextror Study : 2. Test Situations and Water ‘level ecerdan 3. Record Analysis and Data Displays. II PHOTOS OF HIGH WAVES AT PILES. io Gikeeuulase IPatile, : 0 2 Circular and Finned Gime nian pines ; 3. H-Pile with Deep Channels. 4 Conclusions. Sy hes JEJE MEASURED PEAK WATER PATTERNS . 1. Circular Piles 2. Other Piles. 3. Conclusions. IV EXTRAPOLATION OF THE LABORATORY RESULTS. 1. Effects of Pile Confinement. 5 2. Inaccuracies in Modeling the Prototype : 3. Conclusions. V COASTAL ENGINEERING APPLICATIONS . VI CONCLUSIONS. LITERATURE CITED APPENDIX A WAVE-GAGING TECHNIQUES . B TEST WAVE CHARACTERISTICS. C PEAK WATER DATA FOR SINGLE PILES IN SINGLE WAVE TRAIN. D OTHER TEST DATA. E KEY TO REPORTED DATA . TABLES 1 Test conditions and measurements in laboratory studies of wave interaction with vertical surface-piercing piles. Page 69 WS 82 93 167 184 14 CONTENTS TABLES--Continued Major test conditions. Laboratory and prototype situations with identical Froude number . Stagnation regime and Froude number based on obstacle thickness in photo sequences. Runup calculations for MAD Eee io in Figures 21, D2 BG 23o 0 Ge OLAS) ones Wave conditions and percent of pattern variance in Figure 25 . Comparison of angles giving pile channel geometry, 6, half-width of front maximum region, x, and minimum location, 94, for Figure 31. Calculations for [H(8)/H] patterns in Figure 34. FIGURES Usual test situations. Cross sections and types of piles tested . Plan views of the two wave tanks and details of the pile and water level gage configurations. Recorded incident and transformed wave forms in several test situations . Water level record and measured wave dimensions: Wave height, H, crest height, W, and trough depth, Q. Transformed wave dimensions versus orientation angle for four piles. Normalized average crest height around a circular pile [W(a)/W] for two incident crest heights. Crest height over the 180° range of orientation angle for two piles . Camera and pile configurations for photo sequences . Page 16 16 Sif 44 48 56 59 12 13 15 NE) 18 21 22 23 24 10 ital 1° Its) 14 15 16 M7 18 19 20 ail 22 23 24 25 CONTENTS F IGURES--Continued Two photos of wake region behind 1.5-inch circular pile with wave crest incident from top of frame . Measured W(a) in same test situation as Figure 10 . Photo sequence of wave cycle at 3-inch circular pile, with T = 2.32-second wave traveling toward the right and one-eighth second between frames . 9 Incident, ao = 0°, and a = 180° waveforms in same test situation Gis Jala UZ 6 5 6 0 6 600 6 6 6 6086 6 6 6 0 6 0.0 9 0 0 Photo sequence of wave crest striking side-by-side circular and finned circular piles, with one-eighth second between succesSive frames. Photo sequence of wave crest incident into channel of 4x1 H-pile, with one-sixteenth second between successive frames. . Photo sequence of wave crest incident on Sxl H-pile, oriented at 8B = 90°, with one-eighth second between successive frames Three runup regimes at a shallow-draft obstacle with increasing flow velocity, uy @ (assuming no circulation). Bigs aa s [W(B)/W] patterns for five H-piles with maximum horizontal fluid orbit. W(8) patterns for 1x1 and 3x3 H-piles . W(B) patterns for 1xl and 2x2 H-piles Normalized patterns of H(8) and first and second angular differences for 2x2 H-pile in three situations . Photo from rear of disturbance at 2x2 H-pile during crest flow in the 1.5-foot-wide tank . Flow regimes indicated by measured drag coefficient at a circular cylinder. Varying sections to reduce design wave force on pile segment near water surface . Schematic operation of proposed nearshore wave direction gage using a circular pile . Page 50 51 52 53 54 55 57 57 58 61 62 65 66 CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT U.S. customary units of measurement used in this report can be converted to metric (SI) units as follows: a Multiply inches square inches cubic inches feet square feet cubic feet yards square yards cubic yards miles square miles knots acres foot-pounds millibars ounces pounds ton, long ton, short degrees (angle) Fahrenheit degrees by To obtain aaa 25.4 millimeters 24 centimeters 6.452 square centimeters 16. 39 cubic centimeters 30.48 centimeters 0.3048 meters 0.0929 square meters 0.0283 cubic meters 0.9144 meters 0. 836 square meters 0.7646 cubic meters 1.6093 kilometers 259.0 hectares 1.8532 kilometers per hour 0.4047 hectares 1.3558 newton meters 1.0197 x 1073 kilograms per square centimeter 28.35 grams 453.6 grams 0.4536 kilograms 1.0160 metric tons 0.9072 metric tons 0.1745 radians 5/9 Celsius degrees or Kelvins! 1To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use formula: Gis Gy) CE es2i6 To obtain Kelvin (K) readings, use formula: res (G/9) @e =D) = 275, 15- ies I o ii} wD iT} Nn ! U2/2ga u*/gD U2/gt 21/L SYMBOLS AND DEFINITIONS circular pile radius beat length between first and second wave harmonics half-width of wave tank empirical drag coefficient draft of a surface-piercing obstacle stillwater depth eccentric setting on wavemaker drive wheel Froude number Froude number based on circular pile diameter Froude number based on obstacle draft Froude number based on obstacle thickness drag force per unit pile length distance from wavemaker to measurement point acceleration due to gravity wave height horizontal semiaxis of water particle orbit integer index wave number wavelength characteristic flow length trough depth below stillwater level (SWL) Reynolds number Stokes parameter symmetric series curve fit to peak water data SYMBOLS AND DEF INITIONS--Continued wave period obstacle cross-sectional thickness normal to wave direction horizontal fluid speed at wave crest characteristic flow speed crest height above SWL peak water above SWL at angle a on circular pile circum- ference time-averaged quantity of peak water above SWL at angle a on circular pile circumference peak water above SWL at pile yaw angle 8B Maximum pile cross-sectional dimension flow constriction parameter angle specifying point on circular pile circumference yaw angle of noncircular pile average over yaw angles identical according to symmetry angle specifying front symmetry point of pattern angle describing geometry of pile channel kinematic fluid viscosity the transcendental number 3.14... . § fluid density angle locating pattern minimum angle measuring half-width of pattern's front maximum orientation angle in wave basin tests WAVE TRANSFORMATION AT ISOLATED VERTICAL PILES IN SHALLOW WATER by Robert J. Hallermeter and Robert E. Ray I. INTRODUCTION 1. Context of Study. This report presents the results of a laboratory investigation of wave height measurements at an isolated pile. The investigation was motivated by the possibility that wave transformation near a pile can be used to measure nearshore wave directions (Galvin and Hallermeier, 1972). Usual test situations with a straight wave crest incident on a vertical pile, either smooth or with channels, are shown in Figure 1. Figure 2 shows the cross sections and the types of piles tested. These tests investigated the dependencies of transformed crest height near a pile on incident wave characteristics and on the cross-sectional shape and orientation of the pile. This account completes several brief reports on these data (Galvin and Hallermeier, 1972; Hallermeier, 1976; James and Hallermeier, 1976). The tests differed from previous laboratory studies of waves on piles in that the pile's effect on the wave was measured, rather than the wave's effect on the pile. Previous studies primarily investigated wave force or pressure on circular vertical piles (Table 1). The report extends the previous work, as indicated in Table 1, by recording water levels at a wide variety of piles, and thoroughly examining the effects of pile orientation with respect to wave direction. The tests were conducted in relatively shallow water with relatively steep waves; the test piles have small cross sections compared to wavelength. 2. Test Situations and Water Level Records. The tests were conducted in two indoor wave tanks with length, width, and height dimensions of 96 by 1.5 by 2 feet (29.3 by 0.5 by 0.6 meters) and 85 by 14 by 4 feet (25.9. by 4.3 by 1.2 meters), hereafter called the 96-foot tank and the 85-foot tank, respectively. Figure 3 shows plan views of these wave tanks. Each tank had a piston-type wavemaker, a vertical flat plate across the width of the tank, driven horizontally in nearly sinusoidal motion with a set period, T, and amplitude controlled by the radius setting, E, of the rod connecting a rotating drive wheel to the wavemaking plate. At the end opposite the wavemaker, each tank had an unchanging wave absorber, a steep beach of about 3-inch-diameter (0.1 meter) rubble in the 85-foot tank, and a gently inclined plane of permeable rubberized hogshair in the 96-foot tank. A vertical surface- piercing pile was rigidly mounted in the long section of the tanks with constant water depth, d. The major test conditions are listed in Table 2. These laboratory conditions represent the prototype situations listed in Table 3. Sra GeNet Ne = eau — Figure 30. (a) Definition of angle 6 describing channel geometry of pile; (b) hypothetical flow streamlines for yaw angle B <6 and g > 6 (assuming no circulation). As the yaw angle of the pile increases beyond 8 = 8, the flow no longer penetrates the channel to stagnate in the corner; it bypasses the chan- nel. These hypothetical streamlines are applicable only if the water particle excursion is large compared to the channel dimension, so the crest flow approximates steady unidirectional flow. Linear wave theory gives the horizontal semiaxis of the elliptical surface particle orbit as h = W[cosh (kW+kd)]/sinh kd = (U T/2m) . (3) Although the test waves were nonlinear, equation (3) gives the order of magnitude of the fluid excursion, showing it is much larger than X for H-piles with high waves at the medium period (T = 2.32 seconds for d = 1.00 foot; T = 3.55 seconds for d = 2.33 feet). Figure 31 shows peak water patterns measured at five H-piles with maximum fluid excursion. (The 3x3 H-pile is excluded because no data are available for the medium period and pile confinement effects also may be significant for this pile; see Sec. IV.) Table 7 compares the angle 6 for these piles with the angular half- width aod the front runup region in Figure 31; y is defined as the angle at which W(8) drops below %[W(B = 0°) + W]. For the rela- tively ideal situations represented in Figure 31, Table 7 shows a clear relationship between 6 and xX: The five (6; x) pairs have a correlation coefficient of 0.732, so the hypothesis that there is no linear relationship between 6 and X can be rejected with about 81.3-percent confidence (Sec. 13.4.1 in Freund, 1962). 54 0.50 Or: = 0 2x2 H-pile X $30 My 0.25 T=2.32 s d=1.00 ft 0 180° Orientation Angle, B Figure 31. [W(8)/W] patterns for five H-piles with maximum horizontal fluid orbit. 5)) Table 7. Comparison of angles giving pile channel geometry, 9, half-width of front maximum region, yx, and minimum location, 4, for Figure 31. 1x2 H-pile 1xl H-pile 2x2 H-pile 2x1 H-pile 5x1 H-pile The patterns in Figure 31 also show that with deeper channels, the pattern minimums occur at lower yaw angles, and the rear secondary max- imum is higher. Table 7 includes the angular location of the center of the minimum for these patterns. Although the values of @ are less objective than the values of x, the correlation coefficient for the five (6,6) pairs is 0.866, so the hypothesis that there is no linear relationship between © and @ can be rejected with 93.7-percent con- fidence. The relationships between 6, x, and $ can be more firmly established by considering all the [W(8)/W] data sets in Appendix C with clearly defined angles yy and $¢. For the 5 piles listed in Table! 7, there are 25 suitable data sets, giving 50 values of both yx and $. Fitting straight lines yields Me Sos0% + O.50 0, (4) with a correlation coefficient of 0.520, and ¢ = 65.7° + 0.63 6 , (5) with a correlation coefficient of 0.777. Each of these correlation coefficients is large enough to provide 100-percent confidence that there is a linear relationship between 6 and X, and between 6 and 9. Thus, pile channel geometry definitely affects the shape of the peak water pattern for high waves. This conclusion is consistent with the data in Figures 32, 33, and 34, Figures 32 and 33 present peak water patterns for piles of similar shape but different sizes; Figure 32 shows data for low and high waves at T = 1.55 seconds incident on the 1x1 and 3x3 H-piles; and Figure 33 shows data for a high wave at T = 3.10 seconds incident on the 1x1 and 2x2 H-piles. The larger pile generally causes a Slightly higher front maximum, a more sharply defined front maximum region, and a lower rear maximum; peak forward flow is less obstructed by the smaller pile. How- ever, each pattern of a pair is basically similar to the other. 56 Crest Height (ft) Figure 33. 9 30° 60° 90° 120° 150° 180° Orientation Angle, B Figure 32. W(8) patterns for 1xl and 3x3 H-piles. Test conditions: Ws 1.55 seconds, cl S 1,00 soe, GS AS wees 0.3 e tx H-pile 0E90 O 2x2 #H-pile 20 = ©.Oy5 . e = 02 BONE ee — 5 aCe cela wise © eee @ = fo) * e : i) O09 90 Sen eke o0000 es JOR OOOO? = O 564 9590000 oO 30° 60° 90° 120° 150° 180° Orientation Angle, B W(8) patterns for 1x1 and 2x2 H-piles. ie Test conditions: S10) seconds, cle 1500 tee, G > 25 sese, 1 a 4160 snlelies. Th Normalized Second Difference, fie : §& & 0.050 :" ' ’ BS ia 0 Kove t + e@ e Xyy eh yO 2 vx 2 [Ee + 4 x Xx = 0 = Baaen eyes Ketan gt at O) e + - c © 1.0 ——— -- a J 2 a me anon e 2 mare = ‘D> oO oO \ 7 ze Wind Tunnel Measurements \ AA 205 (Roshko, 1961)» “ (=) - Ne 10? 103 10% 10° 108 107 Reynolds Number, R= 2U0/y Figure 36. Flow regimes indicated by measured drag coefficient at a circular cylinder. Roshko (1961) describes the supercritical flow range as characterized by a laminar separation bubble. Proceeding around the pile, the follow- ing phenomena occur: laminar flow separation, transition to turbulent flow, flow reattachment, and finally turbulent flow separation. The laboratory test waves were well ordered, whereas natural waves have a somewhat turbulent character, likely to be important to the flow separa- tion process in this supercritical range. Also, the test piles were smooth, whereas realistic models would have a somewhat rough face, also likely to be important beyond the subcritical range. These other model- ing inaccuracies would be important if these tests had entered into higher Reynolds number flows. 62 The reported tests with circular piles all correspond to the subcriti- cal range, having a larger drag coefficient than intense prototype flows. McNown and Keulegan (1959) stated that increasing wake size is associated with a smaller Cp, so the measured laboratory wakes are generally smaller than prototype wakes. Thus, measured peak water around the rear of circular piles is not generally typical of prototypes included in Table 3. For the noncircular piles tested, the modeling inaccuracies seem to be of minor importance. The piles have small cross sections, measured as X/L, and Section III,2 has pointed out that channel shape has a more important effect than pile size on the shape of the W(8) pattern with these thin piles. Also, the Reynolds number is less important in flow past a pile with channels, because the sharp edges establish the points of flow separation. 3. Conclusions. The wave tanks were wide enough that the reported data are free of significant pile confinement effects except for the 3x3 H-pile in the 96-foot tank. Because the Reynolds number is lower for the reported laboratory tests, measured peak water around the rear half of circular piles is not typical of prototype situations in Table 3. However, the identical Froude number in model and prototype implies the conclusions concerning wave stagnation effects at various piles (Sec. III,3) pertain to prototype situations. V. COASTAL ENGINEERING APPLICATIONS The data in this report (especially App. C) can be used to improve the solutions for the following coastal engineering design problems: (a) Determining deck elevations for pile-supported struc- tures in cases where deck elevation is not limited by other design factors. (b) Improving the design of decks near pile supports in cases where deck elevation will be subject to wave runup at the pile supports. (c) Estimating height to which different types of corro- sion protection is needed on piles and pile-supported structures. (d) Clarifying the physical processes causing the wide scatter in measured coefficients used for computing wave forces on piles. For example, it appears that runup can significantly affect wave force on piles in shallow water when a = U2/2ga = ] (Hallermeier, 1976). (e) Suggesting novel pile shapes for special design requirements; e.g., capping a thick concrete pile with a narrower 63 steel section of equivalent bearing strength to avoid unwanted runup (Fig. 37). If wave direction is nearly constant, as it is in the nearshore zone, web-shaped members may reduce cross section to incoming waves, although transverse oscillations will limit such applications (Apelt and Isaacs, 1968). (f) Estimating wave direction in the nearshore zone. The following paragraphs review the status of the potential use of wave runup at a pile to estimate wave direction. As mentioned in Section I, this study is aimed at evaluating the use of wave transformation at a pile in an instrument measuring nearshore wave directions. In this application, maximizing stagnation effects results in a measurable relief in peak water level on a circular pile's circumference. This relief is symmetrical about the direction of surface flow, and wave direction may be estimated by interpolation, using a small number of water level gages on the pile's circumference. James and Hallermeier (1976) reported dependencies of precision in direction esti- mates on the interpolation method, the angular measurement spacing, the vertical measurement resolution, and the incident wave type. The simplest instrument would use four water level gages spaced 60° apart on the seaward pile half, to measure wave direction within +3° over a 120% range of incidence. This high measurement precision is needed for near- shore wave directions, since wave refraction limits the range of incident direction. The proposed instrument could measure individual crests, recording direction variations. The reported data show that a finned circular pile can produce a smaller angular range of maximum runup than a smooth circular pile. However, this increased relief in water level is associated with a more ragged variation of water level with angle. Thus, it seems doubtful that interpolated estimates of wave direction with a small number of water level gages at a finned pile could attain the precision possible using a smooth circular pile. Figure 38 schematically shows the operation of an automatic direction gage using symmetrical crest transformation at a circular pile. Hallermeier and James (1974) presented an example of the design process for the pile installation, using an estimate of the local wave climate. Major remaining uncertainties about the proposed instrument are a fool- proof objective method for recognizing crest incidence, and whether available water level gages have adequate durability and resolution. Development of a prototype instrument is not presently planned. VI. CONCLUSIONS The principal conclusions from this investigation are as follows: ae With high waves at thin surface-piercing piles, crest stagnation 1s similar at circular and channeled piles (Figs. 14 and 19). 64 Direction Normal \\to Shore Va => Design crest height Rovewerae MWir load a. Tapered circulor pile cap b. Noncircular Pile cap Figure 37. Varying sections to reduce design wave force on pile segment near water surface. 65 ‘aTtd Je[NdAIT9d e Butsn 93e3 UOTIIGITP 9AEM aLOYsSIesu pesodoid Fo uotieLedo dTJeWEYdS “geo saNn3Ty WAV JO 3WIL *‘NOILOSMIG 1S3Y9 ‘SLNSW3UNSV IW ‘TOYLNOD ALINWAD YOLIGS SNIZINDODSY 1S3u 43040934 yO ¥345N8 VLVG ane U3NNVOS MWYYV 399 T3A31 Y3LVM Q3.LNNOW=-3 ld Wd LV SISAIWNY WLVG NOILISINODY Viva 66 b. As in steady unidirectional flow, this free-surface flow effect depends on the Froude number based on peak fluid velocity and the thin dimension of the obstacle. Smooth, breaking, or jetting runup can occur, depending on the Froude number and the geometry of the obstacle's front face (Sec. II,4). c. At a circular pile, wave scattering is overwhelmed by flow stagnation effects when the Froude number, Fy, = (U2/2ga) = (H2/La) , becomes significant compared to unity (Hallermeier, 1976). d. The patterns of measured crest height versus pile orientation with respect to wave direction are largely independent of pile shape. Basically similar patterns are obtained with smooth and channeled piles; all the patterns have a front maximum region, a lesser maximum at the rear, and intervening symmetrically located minimums (Figs. 20 and 26). e. With increasing peak fluid velocity, in patterns normalized by incident crest height, the front maximum becomes higher in a manner consistent with crest stagnation, the rear maximum generally becomes lower, and the minimums become deeper (Figs. 21, 22, 23, 27, and 28). f. Measured runup of a single crest at the front of a thin circular pile agrees well with calculated velocity head, U*/2g (Fig. 4 in Hallermeier, 1976), while mean measured runup in steady wave action is larger than the calculated velocity head (Table 5). However, velocity calculations are problematic for the test waves. g. The patterns show several definite effects of pile shape. The angular width of the front maximum region is linearly related to an angle measuring the shallowness of the pile channels (Fig. 30, eq. 4). The pattern minimums are farthest toward the rear for the smooth piles (flat plate and circular piles), and the minimums are farthest toward the front for deeper pile channels (Figs. 20, 27, 28, and 31; eq. 5). h. Similar stagnation effects are measured in test situations that are geometrically similar (identical Froude number but different scale), although the Reynolds number affects the pattern away from the front maximum region (Figs. 24 and 34). With minor caution, the test results can be extrapolated to prototype situations of interest in coastal engineering (Sec. IV,3). i. A small number of water level gages on the circumference of a circular pile might be used for high-resolution direction measurements of individual nearshore crests (James and Hallermeier, 1976). Available laboratory data permit making major design choices for a field installa- tion (Hallermeier and James, 1974), although several uncertainties 67 remain about the design and durability of an automatic instrument for field wave direction measurements (Sec. V). j. Further study is needed to define surface effects in wave forces on a thin circular pile in shallow water (Sec. V). 68 LITERATURE CITED AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC., Manual of Steel Construectton, 7th ed., New York, 1970. APELT, C.J., and ISAACS, L.T., "Hydrodynamic Force Coefficients for Bluff Cylinders of Tee Shape and Their Relevance to Bridge Piers," Proceedings of the Third Australasian Conference on Hydraulics and Flutd Mechanics, 1968, pp. 169-174. APELT, C.J., and WEST, G.S., ''The Effects of Wake Splitter Plates on Bluff-body Flow in the Range 10+ < R < 5x10*. Pt. 2," Journal of Flutd Mechantes, Vol. 71, Pt. 1, Sept. 1975, pp. 145-160. BARNARD, B.J.S., and PRITCHARD, W.G., ''Cross-waves. 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DAGAN, G., and TULIN, M.P., ''Two-dimensional Free-surface Gravity Flow Past Blunt Bodies,'' Journal of Flutd Mechanics, Vol. 51, Pt. 3, Feb. 1972, pp. 529-543. DEAN, R.G., "Presentation of Research Results," SR-1, Vol. I, Stock No. 008-022-00083, ''Tabulation of Dimensionless Stream Function Theory Variables," SR-1, Vol. II, Stock No. 008-022-00084, Evatuation of Water Wave Theortes for Engineering Appltcatton, U.S. Government Printing Office, Washington, D.C., Nov. 1974. DEAN, R.G., and URSELL, F., "Interaction of a Fixed, Semi-Immersed Circular Cylinder with a Train of Water Waves,'' Technical Report No. 37, Hydraulics Laboratory, Massachusetts Institute of Technology, Cambridge, Mass., 1959. 69 FREUND, J.E., Mathematical Statistics, Prentice-Hall, Englewood Cliffs, N.J., 1962. GALVIN, C.J., Jr., '"Finite-Amplitude, Shallow-Water Waves of Periodically Recurring Form,"' Proceedings of the Sympostum on Long Waves, 1971, pp. 1-32. GALVIN, C.J., Jr., and HALLERMEIER, R.J., "Wave Runup on Vertical Cylinders," Proceedings of the 13th Conference on Coastal Engineering, 1972, pp. 1955-1974. HALLERMEIER, R.J., "Nonlinear Flow of Wave Crests Past a Thin Pile," Journal of the Waterways, Harbors and Coastal Engineering Diviston, Vol. 102, No. WW4, Nov. 1976, pp. 365-377. HALLERMEIER, R.J., and JAMES, W.R., 'Development of a Shallow-Water Wave Direction Gage," Proceedings of the Internattonal Sympostum on Ocean Wave Measurement and Analysts, 1974, pp. 696-712. HELLSTROM, B., and RUNDGREN, L., "Model Tests on Olands Sondra Grund Lighthouse," Bulletin No. 39, The Institution of Hydraulics, Royal Institute of Technology, Stockholm, Sweden, 1954. JAMES, D.F., ''The Meniscus on the Outside of a Small Circular Cylinder," Journal of Flutd Mechantes, Vol. 63, Pt. 4, May 1974, pp. 657-664. JAMES, W.R., and HALLERMEIER, R.J., "'Nearshore Wave Direction Gage," Journal of the Waterways, Harbors and Coastal Engineering Dtviston, Vol. 102, No. WW4, Nov. 1976, pp. 379-393. LAIRD, A.D.K., "A Model Study of Wave Action on a Cylindrical Island," Transactions of the Amertcan Geophysteal Unton, Vol. 36, No. 2, 1955, pp. 279-285. Le MEHAUTE, B., DIVOKY, D., and LIN, A., "Shallow Water Waves: A Compari- son of Theories and Experiments," Proceedings of the 11th Conference on Coastal Engineering, 1968, pp. 86-107. LONGUET-HIGGINS, M.S., ''The Generation of Capillary Waves by Steep Gravity Waves,'' Journal of Fluid Mechanics, Vol. 16, Pt. 1, May 1963, pp. 138-159). LONGUET-HIGGINS, M.S., "A Model of Flow Separation at a Free Surface," Journal of Flutd Mechantes, Vol. 57, Pt. 1, Jan. 1973, pp. 129-148. MADSEN, O0.S., "Waves Generated by a Piston-Type Wavemaker," Proceedings of the 12th Conference on Coastal Engineering, 1970, pp. 589-607. MADSEN, 0.S., "On the Generation of Long Waves," Journal of Geophysical Research, Vol. 76, No. 36, Dec. 1971, pp. 8672-8683. 10 MADSEN, O.S., ''A Three Dimensional Wave Maker, Its Theory and Applica- tion," Journal of Hydraulie Researen, Vol. 12, No. 2, 1974, pp. 205- ZL MAHONEY, J.J., "'Cross-waves. Pt. 1. Theory," Journal of Fluid Mechanics, Wolls S55 ee25 Seats WIS, 96 A2a2ulAl. McNOWN, J.S., and KEULEGAN, G.H., "Vortex Formation and Resistance in Periodic Motion," Journal of the Engineering Mechanics Diviston, Vol. 85, No. EM 1, Jan. 1959, pp. 1-6. MEI, C.C., and UNLUATA, U., "Harmonic Generation in Shallow Water Waves," Waves on Beaches and Resulting Sediment Transport, Academic Press, New York, 1972, pp. 181-202. MORISON, J.R., JOHNSON, J.W., and O'BRIEN, M.P., "Experimental Studies of Forces on Piles," Proceedings of the Fourth Conference on Coastal Engineering, 1953, pp. 340-370. NAGAI, S., TOKIKAWA, K., and ODA, K., "Report on the Pier of the Suspension Bridge Connecting the Main Land with Shikoku Island in Japan,"’ Interim Report I, Hydraulics Laboratory, Osaka City University, Osaka, Japan, 1966. PAAPE, A., and BREUSERS, H.N.C., ''The Influence of Pile Dimension on Forces Exerted by Waves," Proceedings of the 10th Conference on Coastal Engineering, 1966, pp. 840-849. PETRYK, S., 'Drag on Cylinders in Open Channel Flow," Ph.D. Thesis, Colorado State University, Fort Collins, Colo., 1969. ROSHKO, A., "Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number," Journal of Flutd Mechanics, Vol. 10, Pt. 3, May 1961, pp. 345-356. SAUNDERS, H.E., Hydrodynamics in Shtp Design, Vol. I, Society of Naval Architects and Marine Engineers, New York, 1957. SCHLICHTING, H., Boundary-Layer Theory, 6th ed., McGraw-Hill, New York, 1968. SPRING, B.H., "Interaction of Plane Water Waves with Vertical Circular Cylinders,"' Ph.D. Thesis, University of Wisconsin, Madison, Wis., 1973. STAFFORD, R.P., RAY, R.E.L, and JONES, J.C., "Seven Reports on CERC Laboratory Wave Gages,'’ Laboratory Memorandum, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., 1973. TSUCHIYA, Y., and YAMAGUCHI, M., ''Studies of Wave Forces Exerted on Large Cylindrical Piles (1) - Characteristics of the Distribution of Wave Pressure and the Variation of Water Level," No. 14B, Annual Report of the Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan, 1971, pp. 373-390. 7 U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vols. I, II, and III, Stock No. 008- 022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp. WHITE, R.V., and MILLER, R.L., “Experimental System for the Analysis of Continuously Transforming Impulse Waves."' Technical Report No. 10, Fluid Dynamics and Sediment Transport Laboratory, University of Chicago, Chicago, I11l., 1971. lec APPENDIX A WAVE=GAGING TECHNIQUES Both electrical and "direct'' measurement techniques were used to record water levels in the laboratory tests. The electrical gages recorded, on a strip chart, the electrical signal indicating the immersed length of a probe, either by changing resistance (CERC gages) or by changing inductance (the Marsh-McBirney gage). In the direct techniques, wetting of a paper sleeve or erosion of a powder deposit on a circular pile preserved the peak waterline, which was marked with waterproof ink or crayon and then manually measured. This technique measured the entire pile circumference with no important flow obstruction from a sensing probe, but recorded no information on:water level variation in time. The electrical gages were calibrated and used according to well- defined CERC laboratory procedures (Stafford, Ray, and Jonés, 1973). Before use, a calibration in still water ensured that the electrical gage had a suitable linear sensitivity through the expected range of water level. After use, the probe was again dipped in still water to ensure there was no appreciable drift of the gage datum or change in sensitivity. There were no major differences in using the resistance or inductance principles of water level measurement; the exact electron- ics are unimportant. Figure A-1 shows an electronic signal-conditioning unit, a strip-chart recorder, and a standard water level probe. Hori- zontal cross sections of all the electrical probes used are shown in actual size in Figure A-2. White and Miller (1971) investigated the physical considerations in an accurate measurement of fluid level by a surface-piercing probe. They determined that the water and probe surfaces must be kept clean, and that the diameter of the probe and the static meniscus between probe and fluid should be minimized. A probe of minimum diameter approximates a needle piercing the fluid surface, rather than a bluff cylinder; this minimizes the possibility of erroneous measurement due to significant flow obstruction by the probe. James (1974) presented a solution for the shape and height of the static meniscus occurring at an extremely thin circular cylinder due to interfacial tension. For probes of about 0.01- to 0.1-inch (0.3 to 3 millimeters) diameter (see Fig. A-2) in water, the effects due to the static meniscus and flow obstruction should be minimal. Confinement of a probe within a narrow channel was observed to have a Significant effect on its electrical characteristics, but each probe used within a channel was statically calibrated while mounted there. Significant measurement error may arise from the static probe calibra- tion. Water draining off the probe may not exactly follow the water surface; this can be significant when the water level is fluctuating rapidly. Dean and Ursell (1959) reported errors in using static cali- bration factors in wave measurements with a surface-piercing gage. Us Figure A-1. Two-channel strip-chart recorder, standard CERC water level probe, and probe signal-conditioning unit. 74 . Standard CERC Gage D. CERC Strip Gage Conductive Strips ® @ 1.5-in Radius of Curvature . Small CERC Gage E. Narrow CERC Strip Gage Conductive Strips @ © |.5-in Radius of Curvature . CERC Wafer Gage F. Marsh-McBirney Gage 3 ate Support Support Sensor Conductive Surfaces 0) | 2 3 4 (cm) eee es (0) 0.05 0.10 ( ft ) Figure A-2. Horizontal cross sections of electrical water level probes used (in actual size). 75 Noting this possibility, Bourodimos (1968) used a dynamic calibration technique for water level probes, but did not report the magnitude of difference between dynamic and static calibrations. Dynamic measurement errors were not investigated in the present study, so the measured wave- forms have been treated as qualitative data. The major reported data are peak water levels above SWL, and do not include the uncertain accuracy of the instantaneous water level measure- ments. Because peak crest flow varies rather slowly, dynamic measurement errors are unimportant and the static calibration ensures accurate measurement of peak water level. The only major wave-gaging problem in these tests was encountered in making measurements with the strip gages (Fig. A-2, d and e), which were subject to a gain of sensitivity in time. Figure A-3 shows wave, crest, and trough dimensions measured by the incident gage (Fig. A-2,a) and by the strip gage on the pile in one test. This test lasted about 3 hours and the data were collected pro- ceeding counterclockwise from a = 0°. Gage measurements show that the incident wave action did not change during the test, but the strip gage recorded increasing trough and crest dimensions as the test proceeded. The increase in crest height may be due to wetting of the adhesive attaching the conductive strips to the pile face, but the trough measure- ments are puzzling. This problem led to use of the direct methods of peak water measurement at a circular pile. a. Dimensions of Incident Wave. b.Wave Dimensions on Surface of Circular Pile. @ Wave Height & Crest Height e Trough Depth Figure A-3, Measurement drift shown by strip gage on the 3-inch circular pile in unchanging incident wave action. 76 Investigations showed good agreement between electrical and direct measurements of peak water. Figure A-4 displays measurements on the 3-inch circular pile by three techniques in nominally the same test conditions. The three patterns show good basic agreement with slight deviations. Differences could occur because the powder erosion measure- ment is for one wave crest, and because the paper sleeve is rougher than the Plexiglas pile and might cause a different flow boundary layer. Also, the paper might dry slightly before peak water could be marked and the measurement completed. The importance of another possible effect of materials on the meas- urements can be assessed from the W(a) data in Figure A-5. Here a test was repeated with 40 parts per million of wetting agent, Edwal Kwik-Wet, added to the water to reduce effects of surface tension; ob- served average peak water was marked on the Plexiglas pile with a crayon. The two patterns were very Similar, except that the minimums were higher and more symmetrically located without the wetting agent. From these data, it was concluded that the smoothness of the pile material caused no anomalous effects on the data obtained in the model tests. A final possible source of variability in W(8) measurements is the variable probe placement near the pile. The waveforms in Figure A-6 and the associated measurements in Table A-1 provide an estimate of the extreme range in this effect. Four waveforms were obtained deep within and just within the 2x2 H-pile channel at 8 = 0° and 8 = 90°; the two other waveforms were obtained relatively near and far from the flat plate oriented at 8 = 90°. Although the waveforms show definite qualitative effects of gage placement, the peak water level measurements show less than a 4-percent change, which is considered insignificant compared to the variation in W(8) over the range of orientation angle. The major conclusions are: (a) The waveforms recorded by electrical water level gages are somewhat suspect, because the gage response to changing water level is imperfect in an undefined way; (b) measurements of crest dimensions (peak water level) from gage records have adequate accuracy; the agreement between direct and electrical measurements of peak water levels is within about 5 percent. OW e@ Powder Erosion x Electrical Gage ® Wet Paper Normalized Crest Height 0° 20° 40° 60° 80° 100° 120° 140° 160° 180° Orientation Angle, a Figure A-4. Peak water level around 3-inch circular pile measured by three techniques. Test conditions: T = 3.10 seconds, E = 40) anches;, d=" 1200) £00t,1G= 25efeet. 78 008 | "3093 SZ = C8°@, 2 I 9 “SeysUuT O'py = ¥ ‘300F OO'T :SUOTITpuod 3S9], = p ‘spuoses *attd se[stxetg Ie[NdITd yoUuT-¢ }e Jovem yeod poaresqo UO jUSSe BuTIIEM FO 4d9FFq 002! 009 jua6o Buiyyam ynoyyim juabo buijyjom yyiM oO D ‘ajbuy u01jDjUa1I0 00 o00E "G-y emnsTy o0b2 008 | 20 €0 v0 (43) JybIaH 48819 US ( ft ) ( ft) Figure A-6. Waveforms measured with various placements of wave gage probe (see Table A-1 for descriptions of situations). 80 Table A-1. Probe placement effects on measured wave dimension. Test conditions: T = 2.32 seconds, d = 1.00 foot, E = 4.0 inches, G3 25 foGeo* Gage location ws) /i 2x2 H-pile, Deep within channel 2x2 H-pile, Just within channel 2x2 H-pile, Deep within channel 2x2 H-pile, Just within channel Flat plate, 0.25 inch from plate Flat plate, 0.75 inch from plate IMeasurements made using CERC wafer gage (c in Fig. A-2) with resolution of 0.015 W. 81 APPENDIX B TEST WAVE CHARACTERISTICS The following discussion concentrates on wave effects in the 96-foot tank, where most of the reported data were obtained. Regular, high waves were desired for the tests, but the mechanically driven piston generated waves with complicated and variable profiles. Wave variability may be either temporal or spatial. Temporal variability in the wave condition at some point can be caused by irregularities in the generating piston motion over a time large compared to T, or by accumulating reflected wave energy. Figure B-1 shows wave records that should reveal any important temporal variability for a steep wave in the 96-foot tank without a test pile. (The test pile was located near G = 25 feet with the second wave gage close to G = 23 feet in most tests.) There was little change in wave condition when the generator had been running for 1, 5, or 15 minutes, indicating the gently sloping hogshair beach was effectively absorbing incident wave action. Note that the crest height does decrease slightly in time. After After After | 5 15 Minute Minutes Minutes (ft) (cm) (cm) (ft) Figure B-1. Changing wave condition in time after start of 96-foot tank generator. Test conditions: T = 2.32 seconds, Gl NOW) steers, 1k & 41.0 mmenes. There was appreciable reflection off some of the larger test piles (e.g., the 3x3 H-pile), which resulted in a slight variation in the incident wave recorded by the second wave gage at various pile orienta- tions. The incident crest height variation approached (0.05 W), at most, in any reported test; if the gage away from the pile recorded larger 82 variations in the course of a test, the data set was considered to be of unsatisfactory quality. Variations in W(a) or W(8) over the 360° range of orientation angle were always much larger than the variation in W. Some tests required 4 hours to obtain a complete data set, but meas- urements at the beginning and end were usually the same for the same pile orientation. Measurement drift in time was a common problem only with the CERC strip gages (d and e in Fig. A-2); this was evidently due to soaking of the adhesive attaching the strips to the pile face (see Fig. A-3). Thus,'temporal wave variability had insignificant effects on the 96-foot tank data. However, spatial wave variability was marked in the 96-foot tank. Figure B-2 shows the waveform at seven locations along the tank for the highest wave at T = 1.55, 2.32, and 3.10 seconds; measured wave dimen- sions are listed in Table B-1. In each case, there are notable changes in crest height and curvature and in the secondary details of the wave- form; the wave must be regarded as transforming as it propagates in con- stant water depth. Two possible causes of this are nonlinear wave propa- gation effects and departures from the ideal in the wave tank (e.g., variations in tank cross section). The 96-foot tank had considerable imperfections but these were not precisely documented. The tank was dismantled after the tests, so this possible cause of spatial wave varia- bility cannot be evaluated. Figures B-3 to B-6 present waveforms for all the generator settings commonly used in the 96-foot tank tests; measured wave dimensions for Figures B-3, B-4, and B-5 are listed in Tables B-2, B-3, and B-4. Nearly sinusoidal waves of small amplitude and virtually permanent form could be generated; the more complicated waveforms with secondary crests result from nonlinear effects associated with finite wave amplitude. Features of these waveforms agree with the findings of Galvin (1971), except that Figure B-3 shows a secondary crest can exist for d/L = 0.124, which is contrary to his report. However, the secondary soliton (in Galvin's terminology) is very weak, explaining how it could have been overlooked in analyzing motion picture records. Because the generation and propaga- tion of nonlinear shallow-water laboratory waves is a subject of continu- ing interest, these data will be compared to analyses in available literature. Madsen (1971) presented a second-order analysis of the waves created by sinusoidally moving piston, in the case of d/L < 0.1 and the Stokes parameter, S = (HL?/2d3) < 4n“/3, where H is the height of the primary generated wave, a Stokes second-order progressive wave at the frequency of the piston motion. His solution predicts observable secondary waves for S > 21*/3, caused by a second harmonic free wave propagating more slowly than the primary wave; the interference between the primary and secondary waves causes an approximately sinusoidal wave height variation away from the generator with a wavelength of L/2. Mei and Unluata (1972) analyzed the resonant interaction between the first and second harmonics off a sinusoidally moving piston in shallow water, finding the harmonics vary periodically in amplitude, with dimensionless beat length, B/L, exhibiting a complicated dependence on S. Their preliminary experimental 83 3.6242 ft G=B4t G=I26ft G168f G=2I.0f G=25.I ft IEG 14) u: T=1,55 $,E23.0 in (ft) (cm) T=3.10 s, E=4.0 in Figure B-2. Waveforms along 96-foot tank for three steep test waves. Stillwater depth = 1.00 foot. Table B-1. Wave height, H, and crest height, W, of the waveforms shown in Figure B-2. Tt eS i558 JES B82 S T = 3.10 s G H W H W H W (ft) | (ft) | (et) | (ét) | (et) | Gt) | Ct) 4.2 | 0-46 | 0.29 | 0.34 | 0.19 | 0.26 |0.13 8. -41 24 0 . c od dl 84 G=16.8 ft (cm) Figure B-3. T = 1.55-second test waves in 96-foot tank. Stillwater depth = 1.00 foot. Table B-2. Wave height, H, and crest height, W, of the waveforms shown in Figure B-3 (T = 1.55 s, d = 1.00 ft). G = 8.4 ft G = 16.8 ft @ SB Adoll see Wavemaker eccentric, E (in) 0.120 0.178 85 G=8.4 ft G=16:8 ft G=25.1 ft (ft) Figure B-4. T= Stillwater depth = 1.00 foot. Table B-3. Wave height, H, and crest height, W, of the waveforms shown in Figure B-4 (T = 2.32 s, d = 1.00 £t). Wavemaker eccentric, E (in) 86 2.32-second test waves in 96-foot tank. (cm) (ft) 3.10-second test waves in 96-foot tank. = 1.00 foot. Figure B-5. T = Stillwater depth Table B-4. Wave height, H, and crest height, W, of the waveforms shown in aves B35 GP-S SolO-s5 cls. i 5OO aXe). Wavemaker eccentric, E (in) 87 (mm) Figure B-6. Typical wave pulses used in 96-foot tank tests (with 6-inch-diameter pile). T d = 0.35 foot, G = 24.2 feet. = 1.00 second, 88 results showed general agreement with the theoretical expressions for the beat length and the second harmonic amplitude. The present data support these analyses to some extent. Secondary crests are apparent when S is greater than about 10, although the critical value evidently depends slightly on d/L, for 0.05 < d/L < 0.13. When a secondary crest is located halfway between the primary crests, the primary crest is higher and sharper, confirming that the primary and second harmonic waves are in phase there. However, the waveforms for various H at the same (L,d) combination (Figs. B-3, B-4, and B-5) fail to indicate a definite dependence of B/L on S. The waveform exhibits a more complicated fine structure as H increases, but there is no change in location of the secondary features and thus no change in the beat length. Table B-5 gives the beat length between locations of con- structive interference shown in the three steep propagating waveforms presented in Figure B-2. The estimated beat length is approximately 3L/2, three times the prediction of Madsen (1971); however, these esti- mates are somewhat qualitative and pertain to situations more highly nonlinear than the stated range of validity of Madsen's analysis. There may be a slight decrease in beat length with increasing S, as Mei and Unluata (1972) predicted. Table B-5. Beat lengths between primary and second harmonics for three steep test waves in 96-foot tank (estimated from Fig. B-2). Wave period, Dimensionless Dimensionless Dimensionless water depth, Stokes parameter, beat length, d/L HL? /2d3 B/L Several other nonlinear wave effects were observed in the 96-foot tank tests, although no quantitative data are available. After a steep crest passed a test pile, capillary waves were often radiated outward from the front half of the pile. Theoretical treatments by Longuet- Higgins (1963) and. by Crapper (1970) have shown these waves can be gener- ated where surface tension forces are accentuated due to a sharply curved free surface. The blockage of the propagating waveform at the pile causes an increased surface curvature. The resulting capillary waves are visible in some photos in Section II. There was also some flow along steep crests in the 96-foot tank. A slight lump on the crest was observed to bounce from one side of the tank to the other as the crest propagated toward the beach. This lateral flow was apparently neither the transverse wave described by Madsen (1974) nor 89 the cross wave described by Mahoney (1972). Experiments by Barnard and Pritchard (1972) confirmed that a wavemaker moving at frequency wo, exciting a plane progressive wave train with wavelength L, may also generate a standing cross-wave field with frequency w/2 as a result of nonlinear resonance, if the tank width is greater than L. Madsen (1974) experimentally confirmed the possible occurrence of a standing transverse wave at the frequency of the generator motion if the tank width is greater than L/2. The tank width was never as large as L/2 in the 96-foot tank tests, and the lateral flow was observed with b < (0.1)L. The observed flow may have been due to a slight side motion of the somewhat loose- fitting, generating piston, or to the departures of the tank from a con- stant rectangular cross section. Because a slight leakage around the wavemaker can measurably affect generated wave height (Madsen, 1970), an asymmetric leakage could cause a significant initial variation in H across the tank. This, in turn, could cause an important lateral flow close to the generator. W(a) patterns markedly skewed about a = 0° were often recorded at G = 8.6 feet (see Fig. 24), while measurements at G = 25 feet gave patterns that were less skewed, but definitely not symmetric about a = 0° (James and Hallermeier, 1976). Figure B-7 shows typical waveforms in the 85-foot tank tests; measured wave dimensions are listed in Table B-6. The short, steep beach in this tank was highly reflective in certain situations, resulting in marked wave variability both along and across the tank. Figure B-8 shows signif- icant wave variability in the 85-foot tank. At T = 3.55 seconds, d = 2.33 feet, E = 2.5 inches (6.3 centimeters), and G = 19 feet (5.7 meters), the wave action is distinctly different at the incident gage and the test pile locations, although they are separated by only 4.2 feet (1.3 meters) (Fig. 1). With this wave condition, the tank width is about half the wave- length, so this variability might be associated with the standing wave described by Madsen (1974). Other data obtained in the 85-foot tank was marred by an undesirable test situation. At T = 3.55 seconds, with the test pile at G = 30 feet (9.1 meters), the pile was one wavelength from the generator and from the beach toe, so the incident and reflected waves superposed in phase. However, data of certain value were always obtained with wave pulses in the 85-foot tank. From certain other test data for the same tank, it was established that scale effects do not affect the conclusions about wave transformation from these model tests (see S@Eoq III) In summary, the complicated nonlinear behavior of the test waves in the 96-foot tank should have had little effect on the conclusions present- ed in this report, since the transformation in space is not marked over a distance on the order of the pile cross-sectional dimension. The flow at any wave phase is approximately unidirectional for the thin test piles, and the waves may be regarded as having a permanent form locally. The crest height is the important characteristic of the waveform since it de- fines the peak horizontal flow velocity causing the peak water at the pile. Because the crest height varies as the wave propagates, this normalizing factor must be carefully selected for each test situation. The waveform features are of secondary importance to the present study, although the crest curvature in space must influence the accuracy of the unidirectional flow approximation. 90 (ft) : OKs EEzIOnn arn ( ft) Oe E=2.5 in E=4.5 in (ft) E=45 in Waveforms for five typical test waves at field gage Figure! B=. in 85-foot tank. Stillwater depth = 2.33 feet. Table B-6. Wave height, H, and crest height, W, of the waveforms shown in Figure B-7. Test condition "199F 61 = 9 “S@eydUT G°Z = q ‘3005 6¢°Z = Pp ‘spuodce9s Gg°*s = | :SUOTIIPUOD Ysa] *(oTtd 4s93 ou YIM) yUe }OOF-Gg ut 9 {Td pue a3e3 Plot} JO SOTS UseMJOq AITTTGeETICA DALM "g-q oansty BIS aid aS abd pjar4 (45) O72 APPENDIX C PEAK WATER DATA FOR SINGLE PILES IN SINGLE WAVE TRAIN This appendix includes 73 rectilinear plots obtained from a simple computer program. The plots show 148 data sets of measured peak water versus pile orientation with respect to wave direction, with peak water normalized by the incident crest height. The original test records yielded incident crest height and peak water level (at each pile orienta- tion angle), both measured above the SWL. The plots include all data sets surviving a check of internal con- sistency of the test record. This check ensured that the strip-chart record of the incident wave did not display ''excessive"’ change in SWL or wave height during the test. Typically, the sensitivity of the electrical gage was such that incident wave height was recorded at about 35 to 40 lines of the 50 lines on the strip chart. For convenience, an excessive change in height or SWL was defined as two or more lines; changes greater than this complicate the reduction of the test record and the production of accurate normalized plots. This check resulted in the deletion of a large number of data sets obtained in the 85-foot tank. Some of the remaining data displayed nonclosure of the peak water pattern. Measurements at the same 8 at the beginning and end of a test were sometimes appreciably different. Tests were begun at 8 = 0° or at B = 90°, and successive measurements were made at increasing 8. Non- closure was indicated as a jump in measurements near this starting angle, and was apparently due to residual wetting of the wafer electrical gage regularly used at the pile. Some data sets for circular piles showed all normalized peak water measurements below 1.0. This occurred only for wetted paper or powder erosion records with small incident wave height, and was probably caused by a slight error in marking the SWL when the record was made. On the following plots, individual tests are identified by a six- digit alphanumeric code. The first letter is G, W, or E, indicating electrical gage, wetted paper, or powder erosion record of peak water, respectively; tests with a leading E are one-wave records. The second letter is A if the test was done in the 96-foot tank, and B if the test was done in the 85-foot tank. The third character is the last number of the year, between 1970 and 1973, when the test was performed. The final three numbers indicate separate tests done in a certain year. Each following plot shows only data for a certain pile with certain wave period and water depth. 38 OST S33yu930 «' STONE NOILVINATYO Bet D9 0 DS- O02 T- OSt- 6€°D 22°0 xX LOBOS heen), er) S\f0) no} 0° [ So fel oer = Upen jas. 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This appendix discusses these test series, without a full presentation of the | data obtained (the complete data are available at CERC), and presents plots of previously reported data which did not survive the internal consistency check. ; : 1. Tests with Two-Wave Trains on a Single Pile. Early in this study, some tests were conducted in an outdoor three- dimensional wave basin. These tests were initiated primarily to investi- gate scale effects on the measurements. The wave basin tests were plagued by various problems, and scale effect investigations were eventually completed in the 85-foot tank. However, one meaningful series of nine tests was conducted which could not be duplicated in the 85-foot tank. Two wave generators were set to generate wave trains of 1.90- and 2.53-second periods, propagating at right angles past the test pile. Because the periods were in the ratio 5:4, and the generators were ini- tially in phase, the wave trains constructively interfered at the pile with a 7.6-second period (see waveform in Fig. D-1). The peak wave height was measured from the gage record obtained in the pile channel, as the pile orientation was varied over the 360° range. Figure D-2 presents the patterns measured at the 1x1 and 2x2 H-piles in the same two-wave test situation. (The special orientation angle y is defined in Fig. D-2.) These two patterns closely agree. K-20 5 —> WWM tte ANNA Figure D-1. Water level record in test with two wave trains. 167 To Generator 2 —— Figure D-2. @ 2x2 H4-pile ft |r. Generator | | x | H-pile Measured peak wave height patterns at 1xl and 2x2 H-piles in same test situation with two wave trains. Generator 1: T = 2.53 seconds, E = 3.5 inches; Generator 4) sle=) be90 seconds, E = 3.0 inches. Piles were located 10 feet from each generator. 168 Galvin and Hallermeier (1972) introduced the zero-crossing method for determining the front symmetry point of a simple pattern. This uses the zero crossing of the quantity [H(8) - H(8+180°)] or [W(8) - W(8+180°)] to locate the angle separating the front from the back of the pattern; this angle is 90° away from the front symmetry point. Figure D-3 shows [H(W) - H(W+180°)] for the two patterns in Figure D-2. Each pattern has a well-defined symmetry point located in the direction between the two generators. Of the nine tests discussed here, five were run with either one or the other generator operating, and four were run with two wave trains. Figure D-4 shows the ratio of the computed velocity heads’ in the two wave trains versus the measured zero-crossing angle of the resulting peak wave height pattern. (The velocity heads were computed using McCowan's solitary wave theory.) The linear trend in Figure D-4 indicates that simple additive wave stagnation effects dominate the measured pat- terns at these two piles with relatively shallow channels. Also, there is little difference in test results with the two geometrically similar piles of different size. 2. Tests with Closely-Spaced Circular Piles. Some tests were performed with two circular piles centered side-by- side in the 1.5-foot-wide wave tank, primarily to investigate effects of pile confinement. Center-to-center separations were 6 or 9 inches (0.15 or 0.23 meter), the two test piles sometimes had unequal diameter , and a wave pulse including one dominant crest was used. Electrical gages recorded the waveforms 2 feet (0.61 meter) in front of and behind the piles, and the peak waterlines on the piles were recorded by erosion of a powder deposit or wetting of a paper sleeve. The recorded peak water- lines show complicated variability, especially with piles of unequal diameter (Fig. D-5). These tests were basically extraneous to the present study, and no effort was made to interpret the resulting data. 3. Previously Reported Data of Unsatisfactory Quality. Some data presented in Galvin and Hallermeier (1972) and in Figures 20, 27, and 28 of this report did not survive the consistency test (App. C). These data sets are of lower quality than those shown in Appendix C, but are valuable in illustrating qualitative trends. For completeness, the plots on pages 173 to 183 are presented in the standard format used in Appendix C. 169 o w 2x2 H-pile °o I) ro) fo) ‘ o [AY ) AY .180°)), tt ' o ine) ' i Ow 60° 80° 100° 120° 140° 160° 180° 200° 220° 240° Orientation Angle, | xl H-pile 0.1 [FV )-F(Ye180%], Ft 60° 80° 100° 120° 140° 160° 180° 200° 220° 240° Orientation Angle, v Figure D-3. Zero crossings of [H(w) - H(w+180°)] for the two patterns in Figure D-2. 170 1.0 &,, 0.8 =) roe 2 Pr > 0.6 s = [oa 38 04 as => ‘o 2 = 0:2 @/ 7 7 7 7 4 7 A 4 (/ Ae Uf oo y a 4 4 4 7 4 ye e @ 2x2 H-Pile 4 c 7 |} | x | H-Pile 80° 100° 120° 140° 160° 180° 200° Zero-Crossing Angle of [Fc Y)-FLy +180°)] Figure D-4. Ratio of computed velocity heads of two orthogonal wave trains versus zero-crossing angie. 17 ‘yur OPIM-}00F-G*] UT SZojUdD UdeM}9Eq SeYydUT 9 YITM ‘sattd IE[NIITI I9IWeTP-YIUT-G*] OPTS-Aq-9PpTS OM} puNOTe I9zeM yeoq ‘*S-q dan3TY 229353 S335d930 0 SATSNY NOTIGINATYO ost OT 03 a) OSs Ogik= O8t—- 62°08 LTt*0 Xx