DYNAMIC WAVE SETUP IN COASTAL BAYS PART I RESULTS OF AN EXPERIMENTAL INVESTIGATION
T. M. Parchure and
Robert G. Dean
Florida State University Beaches and Shores Resource Center Innovation Park Morgan Building Box 5 2035 East Paul Dirac Drive Tallahassee, FL 32304
1. Report No. 12. 3. Recipient' aAccession No.
4. Title and Subtitle 5. Report sato Dynamic Wave Setup in Coastal Bays August, 1991 Part I Results of an Experimental Investigation 6.
7. Authors) S. Performing Organization Report No. T. M. Parchure UFL/COEL-91/011 R. G. Dean
9. Perforining organization EM~ and Address 10. Project/Task/Vork Unit No.
Coastal and Oceanographic Engineering Department University of Florida 11. Contract or Grant No. 336 Weil Hall A14119 Gainesville, FL 32611 13. Type of Report 12. sponsoring organization Name and Address Final Report, Part I of Florida State University Two Parts Beaches and Shores Resource Center
2035 East Paul Dirac Drive
Tallahassee, FL 32304 14. 15. Supplesientary Notes
An extensive set of experiments was carried out to investigate the effect of inlet geometry on wave setup in a lagoon. The experiments were conducted in a wave basin which communicated with the elliptical planform lagoon by a connecting inlet. The inlet was a channel with a thin aperture of various opening dimensions. Two aperture types were investigated including one which represented a slot extending upwards from a variable
sill depth and the second a "window" which extended from a variable sill depth to a variable soffit level. Setup was measured to within approximately 0.2 mm using a sloping differential manometer. The measurements for each geometry were repeated three or four times and the average presented. The waves were primarily periodic although in one test a crude approximation to irregular waves was generated. Totals of 109 slot geometries
and 168 window geometries were investigated and the results presented in tabular and graphical forms.
Complex dependencies of setup on aperture geometry were found. As examples, for a slot with sill at still water line, the setup increased with slot width. However, for sill submergences of 50 mm and greater, the setup decreased with increasing slot width. The effect of increasing wave heights resulted in an expected increase in setup. For a
"window" of fixed vertical opening, the setup generally decreased with sill submergence, but exhibited a complex dependency on window width. A second analytical
interpretative/predictive report is planned to parallel the experimental results presented herein.
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TION PA GE
DYNAMIC WAVE SETUP IN COASTAL BAYS
PART I RESULTS OF AN EXPERIMENTAL INVESTIGATION
T. M. Parchure R. G. Dean
Florida State University
Beaches and Shores Resource Center
Morgan Building Box 5
2035 East Paul Dirac Drive
Tallahassee, FL 32304
TABLE OF CONTENTS
LIST OF PHOTOGRAPHS . . . LIST OF FIGURES . . . . LIST OF TABLES . . . . NOTATIONS USED . . . . 1. INTRODUCTION . . . . 2. RELEVANCE AND SCOPE OF STUDY 3. LITERATURE REVIEW . . . 4. EXPERIMENTAL FACILITIES . 5. WAVE MEASUREMENTS . . . 6. WATER LEVEL MEASUREMENTS . 7. SUBMERGED SILL AT THROAT .
7.1 Parameters Used .. .. 7.2 General Observations .
. . . . . . . . 3
. . . . o.. . . 3
. . . . . . . . 5
. . . . . . . . 6
. . . . . . . . 7
. . . . . . . . 9
. . . . . . . 10
. . . . . . . 13
. . . . . . . 16
. . . . . . . 18
. . . . . . . 24
7.3 Effect of Inlet Width at Fixed Sill Submergence 7.4 Effect of Sill Submergence at Fixed Inlet Width 7.5 Combined Effect of Width and Depth . . .
7.6 Effect of Incident Wave Height . . . . 8. RECTANGULAR WINDOW AT THROAT . . . . . .
8.1 Parameters Used . .. .. . . . .
8.2 Effect of Window Height and Sill Submergence .
8.3 Effect of Soffit and Sill Submergence . . .
8.4 Influence of Submergence Parameter
8.5 Effect of Window Width . . . .
8.6 Effect of Window Height . . . .
8.7 Effect of Soffit Elevation . . 9. EXPERIMENT USING IRREGULAR WAVES . . 10. DISCUSSION .
11. CONCLUSIONS .
11.1 General .
11.2 Submerged Sill at Throat . . .
11.3 Rectangular Window at Throat . . ACKNOWLEDGEMENTS . . . . .
BIBLIOGRAPHY ON WAVE SETUP . . . . Appendix I: Observations with submerged sill
lagoon inlet . . . . .
Appendix II: Observations with rectangular window at
lagoon inlet .
25 28 28 31 35 35 35 38
42 43 43 48 48 51 57 57 57 58 58 59
LIST OF PHOTOGRAPHS
Photo 1: General view of sea, lagoon and data acquisition
Photo 2: View of lagoon from the shore . . . . . 15
Photo 3: Throat constriction and wave gages in the lagoon . 17 Photo 4: Wave gages in sea 17
Photo 5: Assembly of equipment for water level measurement 20 Photo 6: Water level measurement using inclined manometer . 21
LIST OF FIGURES
Fig. 1: Definition sketch of wave setup (Shore Protection
Manual, 1984) 8
Fig. 2: Schematic layout of experimental facility . . 14 Fig. 3: Wave setup in the lagoon as a function of time . 23 Fig. 4: Effect of inlet width at fixed sill level . . 27 Fig. 5: Effect of sill level at fixed inlet width . . 29 Fig. 6: Correlation between wave setup and submerged area 30 Fig. 7: Effect of wave height and sill submergence for
inlet width of 25 mm. 32
Fig. 8: Effect of wave height and inlet width for fixed
sill submergence of 50 mm . . . . . . 33
Fig. 9: Effect of wave height and inlet width for zero
sill submergence 34
Fig. 10: Effect of window height and sill submergence for
25 mm wide window 36
Fig. 11: Effect of window height and sill submergence for
50 mm wide window 39
Fig. 12: Wave setup as a function of submergence ratio for
25 mm wide window 40
Fig. 13: Wave setup as a function of submergence ratio for
50 mm wide window. 41
Fig. 14: Influence of submergence ratio . . . . . 44
Fig. 15: Effect of window width at fixed sill submergence 45 Fig. 16: Effect of window height at different sill levels
for 25 mm wide window 46
Fig. 17: Effect of window height at different sill levels
for 50 mm wide window. 47
Fig. 18: Effect of soffit elevation of rectangular window
for fixed sill level of 125 mm . . . . . 49
Fig. 19: Effect of window sill on wave setup with window
soffit at still sea level. . . . . . . 50
Fig. 20: Illustration of incident regular waves in the sea 52 Fig. 21: Wave setup in the lagoon under regular waves of
60 mm height. Inlet configuration: Full width,
zero sill submergence 53
Fig. 22: Illustration of irregular waves generated in
the sea 54
Fig. 23: Wave setup observed in the lagoon under irregular
waves. Inlet configuration: Full width, zero sill
LIST OF TABLES
1.1 Effect of sill submergence on wave setup; H = 50 mm,
T =2.2 s 64
1.2 Effect of inlet width on wave setup; H = 50 mm,
T = 2.2 s 65
1.3 Effect of wave height on wave setup at fixed inlet
width = 25 mm, T = 2.2 s 65
1.4 Effect of wave height on setup at fixed sill level
= 50 mm, T = 2.2 s . . 66
1.5 Effect of wave height on setup at fixed sill level
= zero, T = 2.2 s . 66
2.1 Effect of 25 mm wide window on wave setup; H = 50 mm,
T = 2.2 s . . . .. 68
2.2 Effect of 50 mm wide window on wave setup; H = 50 mm,
T = 2.2 s . 69
2.3 Effect of window height of fixed width on wave setup,
sill level fixed at 125 mm. H = 50 mm, T = 2.2 s . . 70
2.4 Effect of sill submergence and height of 25 mm wide
window; H = 50 mm, T = 2.2 s 71
2.5 Effect of sill submergence and height of 50 mm wide
window; H = 50 mm, T = 2.2 s 72
As = submerged area of slot below still water level AW = submerged area of window below still water level b = height of window di = submergence of sill/submergence of window sill below
still water level
d2 = submergence of window soffit with respect to still water
db = depth of water at breaking point g = gravitational acceleration H = incident monochromatic wave height in model Hb = breaking wave height Ho = deep water significant wave height
= equivalent unrefracted deep water significant wave
m = beach slope R = wave runup Sr = submergence ratio = d2 / d, W = width of sill W1 = width of window ?7 = water surface displacement due to wave motion A- = maximum steady state wave setup inside the lagoon
-e = setdown at the breaking zone
Wx = maximum dynamic setup 11W = net wave setup at the shore
DYNAMIC WAVE SETUP IN COASTAL BAYS
PART I RESULTS OF AN EXPERIMENTAL INVESTIGATION
This report is the first of a two-part series which
presents the results of an investigation of the wave setup in interior waters such as bays or lagoons. The current report presents the results of the experimental component of the study and the second report, to follow later, will present the theory and interpretation of the experimental study within the framework of that theory.
A rise in mean water level above the still water level of sea observed in the wave breaking zone on beaches is denoted as the wave setup. A definition sketch of wave setup on a beach and on a berm is given in Fig. 1. Setup occurs where the ratio of water depth to deep water significant wave height ranges from 0.9 to 1.1. The magnitude of wave setup is influenced by the bottom topography and the direction of wave approach in the vicinity of the breaking zone. The component of momentum flux normal to the beach produces setup whereas the component parallel to the beach produces a longshore current. The occurrence of wave setup on an open coast has been confirmed by both theory and field measurements and its magnitude is estimated to be of the order of 20 to 40 percent of the breaking wave height. During extreme storms, dynamic wave setup can be a substantial component of the total storm surge on an open coast. It might be intuitively deduced that the wave setup occurring at the shoreline would propagate into the interior waterways such as coastal lagoons and tidal inlets. However, the extent of such propagation is not yet well-known.
This report presents results of laboratory investigations carried out to measure the dynamic wave setup in a coastal lagoon. Particular emphasis is given to the geometry of throat through which the bay is connected to the sea. Two different configurations viz. submerged sill and rectangular window were tested in a physical model and wave setup in the lagoon was
Normal SWL IyMWL
a) On a Beach.
ormal SWL NewS b) On a Berm or Reef.
=Setdown at the Break Point =Net Wave Setup at the Shore, iLfw= Aft-'Tb = Wave Setup between the Breaking Zone and the Shore = Depth of Water at the Breaker Point = Beach Slope
= Wave Runup above Still Water Level
Fig. 1: Definition sketch of wave setup (Shore Protection
measured for different dimensions and elevations of sills and windows.
2. RELEVANCE AND SCOPE OF STUDY
An accurate estimation of wave setup appears to be necessary in respect to at least four cases noted below:
i) Tidal measurements made in the interior areas of water
bodies connected to sea include an undetermined
wave-induced component which also causes a rise in the sea water level. It is therefore necessary to investigate the
problem of wave setup in interior waterways in order to
separate out the tidal and wave components. This in turn
would lead to a better interpretation and prediction of
ii) It is believed that the variability of wave setup is
responsible for much of the small-scale variability in the
storm surge elevations. An accurate estimation of wave
setup will be valuable in improving the accuracy of already
existing numerical models for the estimation of storm surges (Committee on Tidal Hydraulics, 1980, Hydrology
Committee, 1980, Harris, 1982, Dean and Chiu, 1984). In
studies of coastal flooding by hurricanes, the effect of
wave setup needs to be considered in the water level
iii) The rise in water level caused by wave setup needs to be
included in the hydrostatic pressure contribution while
designing coastal structures. The computation of wave setup
can be an important part of a thorough design effort
requiring water level estimation for major engineering
structures such as nuclear power plants where it is
important to consider all possible causes of water level
iv) Nielson (1988) found that the average water table height
just landward of the Dee Why Beach, Sydney, Australia, was
elevated above the offshore mean tidal level by at least
1.2 m at all times. While 0.5 m of this superelevation is
attributed to the tidal infiltration/draining process, the
remaining rise in water table was due to wave setup and
The scope of this report is restricted to the laboratory measurement of wave setup inside a coastal lagoon. Detailed presentation of laboratory results and the conclusions drawn from the same have been given. No attempt is made to provide analytical expressions which could be used to calculate wave setup for the various conditions used in the laboratory tests. Although the geometry of natural interior waterways is often complex and the incident waves which cause the wave setup are also complex, the present study is restricted to a simple elliptic-shaped lagoon subjected to monochromatic wave action. Irregular incident waves were used only for one experiment. While laboratory studies have been carried out by several researchers on wave setup on open beaches, results of laboratory studies on the measurements of wave setup in the interior coastal waterways are not readily available in the literature. The present study may be the first of its kind.
3. LITERATURE REVIEW
The wave setup effect on open beaches has been studied extensively in the laboratory by Fairchild (1958), Saville (1961), and Bowen et al (1968), among others.
Fairchild (1958) conducted model studies of wave setup
induced by hurricane waves at Narragansett Pier, Rhode Island. The studies were conducted on a 1:75 scale model with a 1:32 beach slope simulated with smooth concrete. The magnitude of wave setup was seen to depend upon the distance from the shoreline (water depth), wave height and wave period. The wave setup increased with wave height at a selected depth and distance from the shore. For a constant deep-water wave height, the wave setup increased towards the shore.
The beach slope has a significant effect on wave setup. While measurable setup was observed with a 1:32 slope, the laboratory results of Beach Erosion Board have reported that for slopes of 1:3 and 1:6 subjected to smaller waves of the order of
0.6 to 1.2 m, there was no setup, instead, there was setdown.
Wave setup commences where the ratio of water depth to deep water wave height ranges from 0.9 to 1.1. The amount of setup landward of this point increases as deep water wave steepness decreases for a given value of deep water wave height. The increasing setup with decreasing steepness occurs in part because waves of lower steepness are associated with decreasing dissipation of wave energy due to breaking. Therefore, more wave energy is available to be converted into potential energy associated with wave setup.
Most of the information related to wave setup has been developed for regular waves. Analytical studies by Lo (1981) showed that an irregular (bichromatic) wave train the dynamic wave setup could be 50 percent larger than that predicted by a static treatment for the largest waves in the wave train. Model studies were conducted in a wave basin at the University of Florida. These indicated that the experimental results were approximately in agreement with the analytical results given by Lo (1981).
The wave setup at the still water level shoreline can be shown to be
= 0.176 Hb (1)
The maximum dynamic wave setup, im across the surf zone can be shown to be approximately
W.a = 0.216 Hb (2)
which includes the dynamic factor of 50 percent and in which Hb is the breaking wave height based on the deep water significant
wave height H., taken approximately as Hb = 0.94 H (3)
Hansen (1978) conducted field studies at the island of Sylt in the North Sea. He has pointed out that in designing coastal protection structures, the static load due to water elevation is as important as the dynamic load due to waves. The field measurements showed that the maximum wave setup can reach up to 30 percent of the incident significant wave height.
Nielson et al (1988) used manometer tubes for measuring mean water levels in the surf zone at Dee Why Beach, Sydney, Australia. The study covered wave heights in the range 0.6 to 2.6 m and the beach slope had a range of 1:10 to 1:17. The data showed that when the setup profile was measured right up to the intersection of water level and the beach, the shape of setup profile was very different from the one predicted by models based on spilling breakers and linear wave theory. The measured profiles of setup steepened sharply near the shoreline. The shoreline setup was found to be of the order of forty percent of the offshore R.M.S. value of wave height when the wave height was less than 1.5 m. For larger waves the shoreline setup increased more slowly with wave height.
Theoretical studies of wave setup have been made by
Dorrestein (1962), Fartak (1962), Longuet-Higgins and Stewart (1960, 1962, 1963, 1964), Bowen et al (1968), Hwang and Divoky (1970) and Goda (1975). Theoretical developments can account for many of the principal processes. However, most of the expressions contain factors which are often difficult to specify in practical problems.
The expression based on theory and analysis of laboratory data is given (S.P.M., 1984) as
_. 0. 5 (HO-) 2 T
= 0.15 db (4) 64 r di,.s
1.56 43.75(1-e-19m)Hb (5) 1+ e-19.m gT2
= net wave setup
Hb = breaker height
db = depth of water at the breaker point
g = gravitational acceleration
T = wave period m = beach slope
H, = equivalent unrefracted deep water significant wave height
It may be noted that only a brief literature review on the
laboratory study, field investigation and theoretical development has been given above. It is by no means complete. However, a comprehensive bibliography on the subject is given at the end of this report which also includes the references cited in the text.
4. EXPERIMENTAL FACILITIES
The studies were conducted in a fixed bed physical model constructed in the large wave basin at the Coastal Engineering Laboratory of the University of Florida, Gainesville. The model was not a simulation of any prototype site. Hence, no specific scale ratios were used. Instead, a simplified elliptic-shaped lagoon having an arbitrary size of 1.8 m x 3.0 m (base dimensions) was constructed with a side slope of 1:10. The lagoon was connected to the sea through a 30 cm wide rectangular throat section and a 30 cm wide approach channel with vertical sides (Fig. 2 and Photo 1, 2). The bed level of the lagoon as well as the channel was 20 cm below the still water level in the sea
- Not to Scale Dimensions represented In meters
Throat Section Throat
_______11 iiiiiiiiiuiiir 1 T
Wave Generator }
Fig. 2: Schematic layout of experimental facility
I - 011
trtm. w 4 t I
Nr JU _/
- ---- ,---- "
Photo 1: General view of sea, lagoon and wave generator
Photo 2: View of lagoon from the shore
portion. The wave generator, located 15 m away from the shoreline, generated regular waves parallel to the shoreline. The sea portion was simulated with contours parallel to the shoreline. The sea bed had a slope of 1:20 with water depth increasing from 0 at the shoreline to 20 cm at the end of the channel. Beyond the channel, the water depth was uniform at 20 cm up to the wave generator. The still water level in the sea was maintained constant by operating a water pump which compensated for the small leakage rate of water from the basin. The geometry of the throat was varied by providing wooden boards which had rectangular openings cut symmetrically about the center. The widths and depths of the openings were varied during the course of experiments. Wave heights were measured by wave gages, and the water levels were measured by an inclined manometer, the details of which are discussed in the following paragraph.
5. WAVE MEASUREMENTS
Capacitance wave gages have been developed in the past at the Coastal Engineering Laboratory of the University of Florida. Four such gages were used as sensors, two located in the sea for measurement of incident wave heights and the other two inside the lagoon for measuring the wave heights transmitted into the lagoon through the narrow throat (Photo 3, 4). The gages were connected to a multi-channel data logger and a PDP 11 computer for data acquisition.
The wave gage calibration facility consisted of a large barrel partially filled with water and an accurate rack and pinion type point gage which was mounted at the top of the barrel. The wave gage could be attached to the point gage and moved up and down in the barrel in order to provide pre-determined variable submergences of the sensor. The submergence could be measured to an accuracy of 0.1 mm, which was sufficient for purposes of the present study. Calibration of each wave gage was carried out for 8 to 10 values of submergence. Regression coefficients were determined for a first order straight line fit to the data points. The calibration data were
Throat constriction and wave gages in lagoon
Photo 4: Wave gages in sea
subsequently used for converting voltages into water levels during the wave measurements.
A wave gage is essentially a device for measuring a rapidly varying water level as a function of time. Wave data were acquired at the rate of 10 Hz over a 12 minute duration. This gave adequate data points for a spectral analysis. The periodic maximum and minimum water levels corresponding to the crest and troughs of the waves were determined from the analysis of water levels and the wave heights were computed from the difference in the consecutive values of maximum and minimum levels.
Although the device used for wave generation created
regular waves, the incident waves on the sea-side of the inlet were not quite uniform because they were affected by waves reflecting from the shoreline, guide walls of the wave basin, inlet constriction and so on. Hence the wave height and wave period were determined from the spectral analysis of wave data. The wave data acquired on the PDP 11 computer were transferred to the VAX computer through a hard line for purposes of analysis and plotting of wave data.
6. WATER LEVEL MEASUREMENTS
The primary measurement for the present study was the rise in water level inside the lagoon relative to the still water level in the sea. Two measurement options were available, viz to measure the water levels in the sea and the lagoon independently or to measure the relative difference between the two levels. Since the magnitude of wave setup was expected to be of the order of a few millimeters, the measurements were required to have a resolution of a fraction of a millimeter.
Possible use of the wave gages already available in the
laboratory was first considered for measuring the water levels. The sensors were placed inside 30 cm diameter gage wells made of p.v.c. pipe. The gage wells had a 2.5 cm diameter hole, the size of which could be regulated by means of a valve provided inside the pipe. The purpose of providing a well around the sensor was to filter out the wave-induced fluctuations of water level and to
measure only the change in mean water level as a function of time. It was noticed that the measurements made with these sensors were not acceptable because they did not have the required resolution and they were also vitiated by electronic noise, the magnitude of which was high relative to the main signal.
No equipment was commercially available for conducting water level measurements to the required resolution. A single-tube inclined manometer was also not suitable for measurement of differential water levels. Hence a commercially available two-tube differential manometer was evaluated. The commercial manometer was designed for use in a vertical position, and its tubes were connected through a box at the bottom, giving horizontal outlets for connecting the tubes to the model. In spite of several continued attempts, it was not possible to flush out all the air bubbles from the manometer tubes and the box and its use yielded erroneous results. Hence the manometer was discarded and an improvised two tube manometer was fabricated in the laboratory workshop (Photo 5). This manometer was provided with fully transparent Tygon tubes over the entire length. It was therefore possible to physically inspect each tube at every setting and to ensure that there were no air bubbles trapped anywhere within the tubes. This differential inclined manometer provided very reliable and consistent readings. Hence it was used for all the measurements reported here.
The manometer scale had a least count of 1 mm. By laying it in an inclined position with a slope of 1:5 (Photo 6), it was possible to obtain a resolution of 0.2 mm. One tube of the manometer was connected to the sea water level and the other to the lagoon water level. The physical wave model was constructed on the existing concrete floor of the laboratory and it was not feasible to install the manometer in a pit which would have to be made below the water level of the wave basin in order to permit gravity flow in the manometer tubes. Hence the manometer had to be installed at an elevation higher than the water level in the wave basin. A small vacuum pump was used for the initial setting
Inclined manometer connected to pump
'~1 ~, ~,i
Assembly of equipment for water level measurement
Photo 6: Water level measurement using incline i manoumeter
of the manometer. By applying a high vacuum, on the order of 50 cm of mercury below the atmospheric pressure, the air bubbles from the system were flushed out along with water into a large sealed conical flask. The vacuum in the flask and the tubes was then gradually reduced to a magnitude of about 10 cm of mercury in order to maintain the raised level of water in both the tubes.
The procedure of conducting experiments and taking
observations was very laborious and time-consuming. The initial condition consisted of filling the sea as well as the lagoon corresponding to the maximum water depth of 20 cm. Hence, without the waves, the water level in both the manometer tubes gave equal readings on the scales. The initial level in the manometer tubes corresponding to the still water level in the sea and the lagoon was arbitrarily adjusted within the range of scales for ease of visual reading. The vacuum in each tube was held constant by closing the air valves provided on each tube. Then waves were generated in the sea which also propagated into the lagoon through the throat section. The wave-induced oscillation of water level transmitted in each tube was dampened by means of clamps which throttled the tubes, thus preventing propagation of wave oscillations but permitting transmittal of mean water level changes. It was ensured that the tubes were not fully closed and that the water levels in both the tubes were effectively connected to the respective water levels for true and representative measurements at all times.
The water level in each tube was observed visually on the
scale and recorded at five minute time intervals from the instant of starting the wave generator. It was noticed that the wave setup always increased steadily over a long period of time before reaching a steady state maximum value. Fig. 3 provides an illustration of the wave setup in the lagoon as a function of time for two inlet widths when the sill submergence was 50 mm. Each experiment was continued over a duration of at least 30 minutes to 60 minutes until repetitive magnitudes of wave setup was observed in the five minute interval observations. The manometer was set accurately at the beginning of each experiment
W = 12.5 mm
o-.---- -0- --o -0-
H =50 mm T = 2.2 sec
W = 300 mm 01= 50 mm
Fig. 3: Wave setup in the lagoon as a function of time
so as to read equal height of water column in both the tubes before starting the waves. The same condition was again checked at the end of each experiment after stopping the waves in order to ensure that the manometer had not been disturbed which could cause a measurement error.
7. SUBMERGED SILL AT THROAT
7.1 Parameters Used
Experiments were conducted in order to evaluate the effect of three main parameters on wave setup, viz the width of inlet, the depth of inlet and the incident wave height. The inlet depth is referred to as the sill level or sill submergence below the still water level.
Widths tested: W = 12.5, 25, 37.5, 50, 100, 150, 200, 250, and 300 mm.
Sill levels tested: di = 0, 12.5, 25, 37.5, 50, 62.5, 75, 100, 125, 150, 175 and 200 mm.
Incident waves: Regular waves with a height of 25, 50 and 85 mm, all with a period of 2.2 seconds.
The 300 mm width corresponds to zero constriction (relative to approach channel width), and the 200 mm sill level corresponds to zero constriction in terms of depth at the throat. The zero sill level implies that the sill was at the same level as the still water level.
The following parameters were kept unchanged during this series of tests:
1. The geometry of the lagoon, i.e. shape (oval shape),
size (1.8 m x 3 m), depth (0.2 m) and side slope (1:10).
2. The width (30 cm) and depth (20 cm) of the approach
channel connecting the shore-based lagoon to the sea. The bed level of the approach channel was the same as the bed
level of the lagoon.
3. Only rectangular configurations were used for the throat
4. The sea water level was constant, giving a water depth of
200 mm in the lagoon. This level, referred to as the mean sea level for convenience, was the still water level with
respect to all wave-induced water level variations.
The small increments in width and depth tested in this series resulted in a large number of experiments, each involving one pair of these two parameters. In order to overcome small variability in the observations, each experiment involving one combination of width and depth was repeated three or four times and the average value of all the corresponding wave setup observations was adopted as the measured setup. This increased the reliability of results considerably. All the laboratory observations are presented in Appendix I.
7.2 General Observations
1. During the initial experiments, the wave setup was measured at several locations inside the lagoon. These observations indicated that at the steady state condition which corresponds to maximum wave setup, the magnitude of wave setup was the same at all locations inside the lagoon. At an open coast, wave setup varies along the beach profile, its magnitude increasing towards the shore. However, along the side slope of the lagoon, there was no change in the wave setup. In view of this observation, wave setup was measured only at the center of the lagoon for all subsequent experiments.
2. The wave setup increased with time after commencement of wave action. A steady state magnitude of wave setup was reached after a time lapse varying from 20 minutes to 60 minutes. The maximum steady state magnitude of wave setup has been used for plotting in all the figures. The details of the transients have not yet been studied.
7.3 Effect of Inlet Width at Fixed Sill Level Submergence
The effect of inlet width on the magnitude of wave setup was measured by providing a constriction (Photo 3) having a width varying from 12.5 mm to 300 mm at constant sill level. The
results obtained are presented in Fig. 4. The incident wave height was a constant 50 mm with a wave period of 2.2 seconds. The results are presented for four sill levels viz dl = 0, 50, 100 and 200 mm.
The following conclusions are drawn from Fig. 4:
1. Two distinctly different trends are seen, one with full
closure of inlet below still water level (di = 0) and the other with partial closure. For zero sill submergence, the wave setup inside the lagoon increased linearly with increasing inlet width (plot A) whereas for submergence greater than zero, the wave setup in the lagoon decreased exponentially with increasing inlet width (plots B, C and D).
2. For a fixed inlet width, the wave setup in the lagoon
decreased with increasing submergence of the sill level. As for example, for an inlet width of 150 mm, the setup values for dl 0, 50, 100 and 200 mm were 9.2, 4.62, 1.46 and 0.83 mm respectively.
3. The limiting condition W = 0 is not realistic because it signifies a fully blocked inlet. However, it may be seen that wave setup values for W = 12.5 mm and 25 mm were the same at each of the three values of di = 50, 100 and 200 mm. In order to interpret this trend, it is assumed that the decreasing value of W approaches zero but is not mathematically zero. Then the constant value of wave setup at very small values of W can be extrapolated to give the result that wave setup would be 7.9 mm,
4.2 mm and 2.9 mm for infinitesimally small value of W at sill levels of 50, 100 and 200 mm respectively.
4. At W = 0, the setup increased with decreasing values of d, in the range of 200 mm to 50 mm. However, the trend did not continue all the way to dl = 0. In fact, setup for d = 0 is lower than the setup at dl = 50 for values of W = 0 to approximately 40 mm.
5. At both W = 0 and dl = 0, the inlet is full closed and the setup has to be zero. The intercept of plot A with the ordinate again needs to be interpreted as the condition with infinitesimally small opening in the barrier at the inlet.
d1 =0 mm
9 A+ -wA
IP 7- A 0m
A 0Td = 2.2 s 4Q:
6 d1 = 50 mm
d 1=100 MM
1 d1 = 200 MM
0 50 100 150 200 250 30 WIDTH OF INLET, W (mm)
Fig. 4: Effect of inlet width at fixed sill level
7.4 Effect of Sill Level at Fixed Inlet Width
The effect of change in sill level of the inlet on the
magnitude of wave setup was tested for three inlet widths, viz. 25, 50 and 300 mm. The sill level below the mean sea level was varied from 0 to 200 mm for each of the three widths. The results of experiments are given in Fig. 5.
The following conclusions are drawn from Fig. 5:
1. The wave setup inside the lagoon increased with decreasing submergence of the sill.
2. As would be expected from the width effect described earlier, wave setup was higher with smaller widths.
3. Two distinctly different trends are noted, one with the full width of the inlet and the other with partial blockage of the inlet. For W = 300 mm, which is the full width, the setup increased rapidly and linearly with decreasing submergence of inlet from 75 mm to zero (plot A in Fig. 4). The increase in setup for the rise in sill level from 200 mm depth to 75 mm was very small. For the condition of partial width viz W = 25 and 50 mm (plots B and C) the variation of setup may be classified in
three zones. For the zones with d, = 0 to 50 mm and di = 125 to 200 mm the change in setup was very small. For the central zone with dl = 50 to 125, a rapid and linear increase in setup with decreasing submergence of sill was observed.
7.5 Combined Effect of Width and Depth
It was seen that the wave setup increased with decreasing
submergence of sill (Fig. 4) and with decreasing width (Fig. 5). The combined effect of these two parameters is represented by the area of opening below the mean sea level. Results of all the available data have been used in Fig. 6 for plotting wave setup
as a function of the product of W and d, which gives the area of opening below still water level. It is noted from the figure that wave setup increases with decreasing area of opening, the dramatic increase being in the range closer to zero. No particular trends with respect to the individual parameters W and di were noticeable. All the data points are bound by a relatively
12 11 10
8 -H = 50 mm T 2.2 sec
4 A W=25 mm
2 W =50 mm
1 W = 300 mm 00
0 25 50 75 -1 uu 125
SILL LEVEL BELOW STILL WATER, d1 (mm) 5: Effect of sill level at fixed inlet width
* 300 mm VARIAB 050 mm VARIAB x 25mm VARIAB a VARIABLE 200 mm
* VARIABLE 100 mm 3 Y VARIABLE 50 mm
xX Limits of Envelope
LE LE LE
H=50mm T = 2.2 sec
SUBMERGED AREA BELOW STILL WATER (cm2)
Fig. 6: Correlation between wave setup and submerged area
narrow envelope and a mean line between the upper and lower limits could possibly be drawn to represent the relationship between wave setup and area of opening.
7.6 Effect of Incident Wave Height
The influence of incident wave height was tested for three wave heights viz 25, 50 and 85 mm having a wave period of 2.2 seconds. In Fig. 7, the inlet width was constant at 25 mm and sill submergence varied whereas in Fig. 8 the sill submergence was fixed at 50 mm and inlet width was varied. The trend of increased wave setup in the lagoon with smaller sill submergence and smaller width is the same as observed before. At any given sill level as well as at any given width, the influence of incident wave height is quite substantial. For instance, at 100 mm sill submergence (Fig. 7), setup increased from 0.83 mm at 25 mm wave height to 4.18 mm and 8.36 mm at incident wave heights of 50 and 85 mm respectively. Similarly, for 100 mm inlet width (Fig. 8), setup increased from 1.04 to 5.85 and 8.36 mm when the incident wave height increased from 25 mm to 50 and 85 mm respectively.
The influence of wave height at zero sill submergence is shown in Fig. 9 which shows interesting results. The setup increased with increasing wave height. The setup also increased with increasing inlet width however, the rate of change was quite different depending upon the magnitude of wave height. Plot A in Fig. 9 is the same as plot A in Fig. 4 drawn to a different scale. While plot A which represents the condition of 50 mm wave height is linear for practical purposes, the trends shown by plot B (H = 25 mm) and plot C (H = 85 mm) are quite different. With a small wave height of 25 mm, setup increased from 2.72 to 5.43 mm when the inlet width changed from ~25 to 300 mm. With a larger wave height of 85 mm, setup increased dramatically from 12.1 to 19 mm with a relatively small increase in inlet width from 25 to 75 mm. For any further increase in width up to reaching the full open condition, there was no change in the magnitude of setup.
W = INLET WIDTH = 25mm H = WAVE HEIGHT = 25/50/85 mm T = WAVE PERIOD = 2.2 sec
H-= 85 mm
H = 5mmm
0 25 50 75 100 125 150 175
SILL LEVEL BELOW STILL WATER, d1 (mm)
Fig. 7: Effect of wave height and sill submergence for inlet
width of 25 mm
H = 25 mn,
H = 25/50/85 mm A di = 50.0 mm T = 2.2 sec
H=85 mm H =50 mm
100 200 INLET WIDTH, W (mm)
Fig. 8: Effect of wave height and inlet width for fixed sill
submergence of 50 mm
H =50 mm
H =25 mm
I I I I I I I I I
I I I I I
0 100 200 300 INLET WIDTH, W (mm)
Fig. 9: Effect of wave height and inlet width for zero
8. RECTANGULAR WINDOW AT THROAT
8.1 Parameters Used
When a submerged sill is provided at the inlet, wave energy
is transmitted into the lagoon through the water column above the sill. For academic interest, it was decided to examine the effect of blocking the upper part of the water column by providing a rectangular window in the barrier instead of a rectangular slot. While siltation at the inlet results in creating the effect of a raised sill at natural inlets, an opening in the form of a window can hardly be visualized in actual situations. However, it is hoped that the model results will be helpful in evaluating analytical expressions on the propagation of wave energy through restricted openings.
In this series of experiments, the following parameters were varied and the wave setup was measured for different combinations, repeated here for convenience:
i) Width of window: W1 = 25, 50, 100 mm
ii) Sill submergence: dl = 0 to 200 mm
iii) Window height: b = 25, 50, 75, 100, 125 mm.
This in turn affected the
elevation of window soffit.
iv) Incident waves: Regular waves with a height of
25,50, and 85 mm and a period of
Results of all the laboratory observations are presented in Appendix II.
8.2 Effect of Window Height and Sill Submergence
In this series of experiments, a window of fixed size, 25 m x 25 mm, was moved vertically within the water column below still water level at the inlet and wave setup inside the lagoon was measured for each submergence of window sill.
Fig. 10 shows the effect of window height and sill
submergence on wave setup inside the lagoon for a 25 mm wide window. Two distinctly different trends are seen, the first with window height of 25 mm (plot A) and the other with window heights
WINDOW SIZE (mm)
W b Plot
- 025 x 25 A
-- 25 x 50 B
- x25 x 75 C
-- 025 x 100 D
-- 25 x 125 E
W1 = 25 mm
T = 2 2 se
75 100 125 150
BELOW STILL WATER, d1
Fig. 10: Effect of window height and sill submergence for
25 mm wide window
greater than 25 mm (plots B, C, D and E). The difference is mainly at the sill levels of zero and 25 mm below still water level. When the window sill is at zero, the entire window is above the still water level; however, in the case of a 25 mm window height, the full crest of the wave does not pass through the window. Since the height of incident waves was 50 mm, the clapotis formation or the antinode at the vertical barrier resulted in the crest of the wave being 50 mm above the still water level whereas the window soffit was at 25 mm above the still water level. When the height of window was 25 mm and the sill level was 25 mm below the still water level, the window soffit was located at the still water level and the entire window was just submerged below the still water level. Under both the above conditions, it appears that perhaps the rate of outflow from the lagoon is greater than in the conditions when the window is fully submerged at greater depths and hence the wave setup is smaller for the 25 mm x 25 mm size window when the sill levels are zero or 25 mm below still water level.
Another interesting feature in Fig. 10 is the constant
magnitude of setup observed for all other window heights with sill level at zero (plots B, C, D and E). This is obvious because with a window height 50 mm or greater, there is no obstruction to the wave crest as far as the incoming wave energy is concerned and no change in the outflow from the lagoon because there was free surface flow over a sill with fixed submergence.
Plot B in Fig. 10 represents conditions with a window height of 50 mm. Lower wave setup is observed for sill submergence between 0 and 75 mm. The reason for this is believed to be the same as that explained above for the 25 mm high window.
Consider the plots C, D and E for the window heights of 75, 100 and 125 mm. The trend of variation in setup may be viewed in the following four groups of sill submergence i) di = 0 to 25 mm Wave setup is constant irrespective of the variation in b.
ii) di = 25 to 100 mm Wave setup increases with increasing values of b.
iii) dl = 100 to 150 mm Transition zone. iv) dl = 150 to 200 mm Wave setup decreases with increasing values of b.
When the window sill is at the bottom of the inlet (dl = 200 mm), wave setup continues to increase consistently with decreasing values of b for the entire range of b from 125 mm to 25 mm.
These observations are intriguing and no attempt is made to offer any explanation for this type of variation at this stage. Fig. 11 shows similar observations for a 50 mm wide window with variations in window height b and in the sill submergence di. Again two distinctly different variations are seen. Plot A for b = 25 mm is different from all the rest and plot B appears to be a transition. Plots C, D and E can again be considered as one group with trends similar to those for the 25 mm wide window. Even the four groups of sill submergence are about the same in terms of the sill submergence values.
8.3 Effect of Soffit and Sill Submergence
In order to evaluate the combined effect of window height
and sill submergence, two parameters are proposed, viz dj, the submergence of window sill and d2, the submergence of window soffit below the still water level. The window height parameter is included due to the relationship b = di d2. The observed wave setup is plotted as a function of the ratio of d2/d, in Figs. 12 and 13 for the window widths of 25 and 50 mm respectively. Although a considerable scatter in the data points is seen, there is an unmistakable trend in both the figures. The wave setup continually decreases with increasing values of the ratio d2/dj. In the limits, we have d2/d, = 1 at one end, giving b = 0; and d2/d, = 0 at the other end, giving soffit submergence d2 = 0. From both the figures it is seen that setup would be maximum when d2/d, = 1 i.e. when b -+ 0. It is seen from Fig. 12 that setup was minimum at d2/d, = 0. 2 when the window width was 25 mm whereas from Fig. 13 it is seen that setup was zero at d2/d, =
0.2. This again is a very interesting condition because at d2/d,
WINDOW SIZE (mm) W b Plot 9 0 50 x 25 A A 50 x 50 B x 50 x 75 C o 50 x 100 D 8 V 50 x 125 E W1 =50mm H = 50 mm 7 T =2.2 sec
0 25 50 75 100 125 150 175 2 0
SILL LEVEL BELOW STILL WATER, d1 (mm)
Fig. 11: Effect of window height and sill submergence for
50 mm wide window
d 1= SUBMERGENCE OF SILL BELOW STILL WATER
d2 = SUBMERGENCE OF SOFFIT BELOW STILL WATER
Still Sea Level
200 mm Ib d11
CA) W1 = 50 MM
-13A di and d 2 = Variable H=50mm AA
- 0 T=2.2sec
di (mm) A 200 o 175 x 150 0 125 V 100
A 50 V <50
I I ~I I I I I I I I I ~I ~ I I
0.4 0.2 0 -0.2
SUBMERGENCE RATIO d 2 / d1
Fig. 12: Wave setup as a function of submergence ratio for 25 mm wide window
I I I I I I I I I I I I I I I I
12 11 10
.4 0.2 0 -0.2 -0 SUBMERGENCE RATIO d 2 / d1
d, (mm) A 200 o 175 x 150 o 125 V 100
* 75 0 62 A 50
di = SUBMERGENCE OF SILL BELOW STILL WATER
d2 = SUBMERGENCE OF SOFFIT BELOW STILL WATER
Still Sea Level
200 mm Ib id
W1= 50 mm
-d and d2 = Variable 0H =50 mm
T =2.2 sec
0 0 A
1 0 11 1A
Fig. 13: Wave setup as a function of submergence ratio for 50 mm wide window
= 0.2, the 50 mm wide window had a height of 100 mm and the sill and soffit were located at 125 mm and 25 mm depth respectively.
Thus, d2 = 25 mm, di = 125 mm, b = 100 mm and W, = 50 mm gave the unique combination for which a wave height of 50 mm yielded a zero wave setup inside the lagoon.
For the same ratio d2/d, = 0.2, the wave setup for 25 mm
window is not zero, but it is the minimum and the ratio may have some physical significance. When the window height is large and the sill submergence is low, the window soffit can be above the
still water level, in which case d2 is negative. Wave setup values for negative values of d2/d, are also plotted in Fig. 13. It is seen that while setup in the lagoon continually decreased when the values of d2/d1 decreased from 1.0 to 0.2, it then increased in the range of d2/d, values from 0.2 to -0.8. When the window sill is raised above the bottom, in the limiting condition, the sill could be located at the still water level with the entire window above the still water level. In this case, dl = 0 and the ratio d2/d, becomes o. However, it may be noted that when the window sill is at the still water level, the window soffit reaches an elevation above the wave crest with increasing height of window. Hence, any further increase in b does not change the wave setup. Thus, there is a maximum value for wave setup for values of d2/d, decreasing from 0 to o. For the 50 mm wide window, the experiments showed this value to be 7.1 mm. For the 25 mm wide window, the maximum value of wave setup at d2/d
- oo is 6.9 mm.
8.4 Influence of Submergence Ratio Parameter
As already mentioned earlier, d2 represents submergence of window soffit whereas di represents submergence of window sill. The window height b is given by
b = d-d2 (6)
This can also be written as
b = d -) dl (7) d,
The ratio d2/d, is denoted as the submergence ratio parameter
Sr = d2/d, (8)
b = d, Sd, (9)
The influence of Sr needs to be carefully noted. For fixed value of Sr, the sill submergence d, can be changed by suitably changing the window height. For each ratio of Sr, window height b increases with increasing sill submergence. For a fixed sill level, window height b decreases with increasing values of Sr because b has to decrease for increasing d2 and hence, Sr, when d, is fixed.
Wave setup as a function of sill submergence and the
submergence ratio is shown in Fig. 14 for a fixed window width of 25 mm, and fixed wave height and period of 50 mm and 2.2 sec,
respectively. It is seen that for a fixed Sr, wave setup initially decreases with sill submergence and then remains constant. Also, for a given sill submergence, wave setup decreases with decreasing values of Sr.
8.5 Effect of Window Width
Effect of window width for a fixed sill submergence of 125 mm is shown in Fig. 15 for fixed wave height and period of 50 mm and 2.2 sec, respectively. Wave setup is plotted as a function of
Sr. It is seen that for a given Sr, wave setup is greater with a smaller window width.
8.6 Effect of Window Height
Wave setup as a function of window height is plotted in
Figs. 16 and 17 for 25 mm and 50 mm wide window respectively. It
Note: b Increases with d1 for each ratio of d2 / d1
d decreases with d2/ d1 for each sill level
0 25 50 75 100 125 150 175 200
WINDOW SILL LEVEL BELOW STILL WATER, d1 (mm)
Fig. 14: Influence of submergence ratio
d2 = Submergence of Sill
d1 = Submergence of Soffit /d2 \
b = Window Height = (d1- d2) = d- x dj
-d 2 W1--4
--- ------- 0-50
ST = 2.2 sec
Still Sea Level 11 -W1-d
200 mm Ib jj b dl 10 -_ d- SOFFIT SUBMERGENCE W1= 25 mm /50 mm d1 SILL SUBMERGENCE
9 H =50mm
T =2.2 sec d1= 125 mm E d2 Variable
[b =zero, when d2 /d1 =1]
Ul ~ 5
W1= 25 mm
W-,= 50 mm
1 0.8 0.6 0.4 0.2 0 -0.2 SUBMERGENCE RATIO, Sr d2/di
Fig. 15: Effect of window width at fixed sill submergence
0 Still Sea Level
0 ~200 mil
d1= 50 mm
W1= 25 mm H =50mm T = 2.2 sec
d1= 125 mm
1= 2-0-,op d = 200 mm
HEIGHT OF WINDOW, b (mm)
Effect of window height at different sill levels for 25 mm wide window
d= 50 mm
E \ Still Sea Level
5 200 mm rIb C1
w,=50mm 4 -H =50mm U) T =2.2 sec
di 125 mm
d= 200 mm
0 50 100 150 200
HEIGHT OF WINDOW, b (mm)
Fig. 17: Effect of window height at different sill levels
for 50 mm wide window
is seen that for sill submergence of 50 and 125 mm, the wave setup decreases with increasing height of window. After reaching a minimum, the setup continued to -increase and reached a maximum value. However, the variation for full sill submergence, i.e. for sill located at the channel bed, the variation in wave setup was different. The setup continued to decrease and stayed at the minimum value for subsequent increase in b.
8.7 Effect of Soffit Elevation
Experiments were conducted for different heights of a window of fixed width with its sill elevation fixed at 125 mm. This changed only the soffit level of a window. The results are shown in Fig. 18 for windows of three different widths, viz 25, 50 and 100 mm. It is seen from the figure that for all the three window widths, wave setup was the lowest for a window height of 100 mm.
Experiments were also conducted with two window widths (25 and 50 mm) by keeping the soffit at fixed elevation, viz at the still water level. In other words, the height of window was extended below the still water level, thus changing only the sill
submergence di. The results shown in Fig. 19 show that the wave setup decreased when the window sill level was changed from 0 to
100 mm. The wave setup was unchanged in the range of di values from 100 mm to 200 mm.
9. EXPERIMENT USING IRREGULAR WAVES
The wave generator in the basin was not designed for making random waves. However, it could be operated manually for a short time to generate wave groups of varying heights. The electric drive was turned on for 12 seconds and turned off for the next 5 seconds. This sequence of operation was repeated 20 times in order to provide a very rough approximation to wave groups. The data on incident waves in the sea as well as on the transmitted waves in the lagoon were collected in digital form using a computer-controlled data acquisition system. A time series of each of the data was plotted later for examination. Since the scope of the present study was restricted to the measurement of
Still Sea Level V
1 = 125 mm
d1= 125 mm
H = 50 mm
W1= 25 mm
- x w1= 100 m
HEIGHT OF WINDOW, b (mm)
Effect of soffit elevation of rectangular window for fixed sill level of 125 mm
Still Sea Level
W1=25 mm H = 50 mm T = 2.2 sec
Note: Since d = Zero,
& d2 /d =Zero
W= 25 mm
W= 50 mm
25 50 75 100 125 150
WINDOW SILL LEVEL BELOW STILL WATER d1
Fig. 19: Effect of window sill on wave setup with window soffit
at still sea level
I I I I
1 0 0
wave setup under regular incident waves, only one experiment was conducted with irregular incident waves. A comparison of the results obtained with regular and irregular waves is given.
Fig. 20 shows the train of regular incident waves in the sea with a height of 60 mm and a period of 2.2 seconds. Fig. 21 shows simultaneous wave observations inside the lagoon. In spite of the generation of incident waves as regular waves, the wave pattern in the lagoon appears to be a mixture of large and small waves. This is believed to be the effect of spurious higher harmonics due to nonlinear processes. A continuous increase in the mean water level in the lagoon is easily noticed. After a lapse of 340 seconds, which was the total duration of test, the mean water level still had a rising trend. A steady state would have reached if the test had been continued long enough. The wave setup reached during the test duration was 10 mm.
Fig. 22 shows the irregular waves generated in the sea by manually operating the regular wave maker as described earlier. Fig. 23 shows wave setup observed simultaneously in the lagoon under these irregular incident waves. A continuous rise in the mean water level is again noted. A steady state magnitude would have been reached if the test had continued beyond the test duration of 340 seconds. The wave setup reached during the limited test duration was 5.3 mm. The wave gages were specially tested over long term to check whether they had any drift as a function of time. These tests confirmed the absence of any drift. Hence, the measurements presented in Figs. 21 and 23 confirmed the rise in the mean water level in the lagoon.
The experiments described above were conducted with a wave
height of 50 mm. Assuming that the wave crest and wave trough are symmetrically located around the still water level, the deep water wave trough would be above the constriction at all sill submergences greater than 25 mm. It is obvious that there is a net mass transport of water from the sea into the lagoon caused by the progressive waves. With the rising phase of water level
U m 60 mm ktWO -L 20 f fi
_j-40S 0 50 100 150 200 250 300 330
Fig. 20: Illustration of incident regular waves in the sea
50 100 150 20M5030M3
Fig. 21: Wave setup in the lagoon under regular waves of 60 mm height. Inlet
configuration: Full width, zero sill submergence
.1... I I
Fig. 22: Illustration of irregular waves generated in the sea
Ln U) M5.3 mm CC W 0
0 50 100 150 200 250 300 330 TIME (sec)
Fig. 23: Wave setup observed in the lagoon under irregular waves. Inlet configuration:
Full width, zero sill submergence
between wave trough to wave crest, sea water enters the lagoon whereas during the receding phase from crest to trough, water from the lagoon goes out to the sea. It was observed that the water level in the lagoon continued to rise over an interval of time after starting the waves and then reached a steady state maximum value. The storage of water in the form of wave setup is a result of the difference in the average volumes of inflow and outflow over one wave period. During the initial portion of the period, while water is steadily flowing into the lagoon, the volume of water entering the lagoon must have been greater than the volume of water draining out from the lagoon into sea during the later portion of each wave period. The process continues until a sufficient hydrostatic head is built inside the lagoon which increases the outflow to match the inflow over each wave period and the steady state maximum rise of lagoon water is achieved.
Wave setup is a phenomenon involving the action of a train of many waves over a sufficient period of time to establish an equilibrium water level condition. The exact amount of time for equilibrium to be established is unknown. On an open coast, a duration of one hour is considered an appropriate minimum value (SPM, 1984). Very high waves in the spectrum are too infrequent to make a significant contribution in establishing wave setup. Hence significant wave height represents the condition most suitable for design purposes. The time factor in establishing wave setup has also been noted by Fairchild (1958). Under the present laboratory study it was noted that the wave setup inside the lagoon increased rapidly during the first 5 minutes, then increased gradually over the next 15 to 45 minutes and finally maintained a steady state maximum value which did not change in spite of the continued wave action (Fig. 3). The time required to reach equilibrium would be a function of several parameters such as the size of lagoon, size of throat opening, magnitude of incident wave height, etc.
1. The wave setup inside the lagoon was uniform over the entire area of the lagoon including the side slopes. Thus wave setup inside the lagoon was not location-dependent.
2. The wave setup increased with time after commencement of wave action. A steady state magnitude of wave setup was reached after a time lapse varying from 20 minutes to 60 minutes. This was observed for both regular as well as irregular incident waves. The maximum steady state magnitude of wave setup has been used for comparison of results with different test conditions.
11.2 Submerged Sill at Throat
1. Wave setup inside the lagoon increased with smaller submergence of the sill for a constant inlet width and with smaller inlet width for a constant sill submergence.
2. Wave setup increased with increasing wave height for a constant sill level or for a constant inlet width.
3. When the sill was located at the still water level, wave setup inside the lagoon increased linearly with the width of opening.
4. Wave setup in the lagoon increased rapidly with
decreasing area of opening below the still water level. It is apparent from Fig. 6 that setup would be maximum when the submerged area below still water level is zero. Since zero area means complete blockage of the inlet, there cannot be any setup inside the lagoon. However, it has been pointed out earlier that the setup increases with smaller depths and also with smaller widths. Hence zero area needs to be interpreted as the condition with infinitesimal values for both width and depth. This condition has a finite maximum value of wave setup inside the lagoon.
5. Zero depth condition has a physical significance in that the sill level is the same as the still water level. Zero width condition would imply that the inlet is fully closed and there should be no setup. However, this again needs to be interpreted
as the condition with infinitesimally small width of window which has a finite maximum setup.
6. For a fixed width and depth at the inlet, wave setup increased with increasing wave height.
11.3 Rectangular Window at Throat
1. The relationship of wave setup with varying window height and varying sill level is rather complex, as may be seen from Figs. 10:and 11. It is difficult to describe it briefly in generalized simple terms.
2. For a constant submergence of sill, wave setup decreased with increasing height of window and then increased again (Figs. 16 and 17).
3. The wave setup decreased with increasing submergence of
window sill below the still water level and then increased in the range closer to the full depth.
4. The Submergence Ratio, defined as the ratio of
submergence of window soffit to the submergence of window sill, could be used as a parameter for demonstrating the effect of other parameters (related to submerged window) on the magnitude of wave setup (Figs. 12, 13, 14 and 15).
5. For a fixed submergence ratio and fixed sill submergence, the setup increased with increasing incident wave height.
The financial support provided by Florida State University, Beaches and Shores Resource Center under contract number A14119 for conducting the study is appreciated. Typing and drafting drafting assistance provided by Cynthia Vey and Lillean Pieter, respectively, are appreciated. Thanks are due to the staff of the coastal engineering laboratory for the help rendered in construction of the model and in setting up the instrumentation.
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Observations with submerged sill at the lagoon inlet
1. d, = submergence of sill below still water level
2. Incident waves for all the measurements reported in Appendix
I were regular waves with a height of 50 mm and a period of
2.2 sec except where the wave height is stated as 25 or 85
3. Observations under each test were continued until a steady
state value of maximum wave setup was reached. Each test was
conducted three or four times. Results reported in
Appendix I are the average values of the steady state setup
of all the tests for each condition.
Table 1.1: Effect of sill submergence on wave setup; H = 50
mm, T =2.2 s
Maximum Wave Setup,
W = 25 mm W = 50 mm
2.92 2.92 2.92
3.34 4.18 5.22 6.26
6.47 6.47 6.69 6.90 7.10
W = 300 mm
0.83 1.25 2.30 2.72
200 175 150 125 100 75 62.50 50
Table 1.2: Effect of inlet width on wave setup; H =
= 2.2 s
50 mm, T
d = 50
2.92 2.92 3.13
4.62 5.85 6.06
Setup, An (mm)
dl = 100
1.04 1.46 2.09 2.30 2.71
Table 1.3: Effect of wave height on wave setup at fixed inlet
width = 25 mm, T = 2.2 s
Maximum Wave Setup, An (mm) d1 H = 25 mm H = 50 mm H =85 mm mm
200 0.63 2.92 6.90 175
150 0.63 2.92 7.30 125 3.34 100 0.83 4.18 8.36 75 5.22
50 1.88 6.50 10.03
0 2.72 6.91 12.12
With dl = 0
200 150 100 75 50
9.40 7.50 7.10
6.48 6.90 6.70
With dl = 200
0.42 0.63 0.83 1.36 1.67 2.92 2.92
Table 1.4: Effect of wave height on setup at fixed sill level
= 50 mm, T = 2.2 s
Maximum Wave Setup, H = 25 mm H = 50 mm
0.42 1.04 1.88
H = 85 mm
4.81 6.27 7.52
Table 1.5: Effect of wave height on setup at fixed sill level
= zero, T = 2.2 s
Maximum Wave Setup, AM (mm)
W H = 25 mm H = 50 mm H = 85 mm mm
300 5.43 11.50 18.80 250 10.03
200 9.41 150 3.34 9.19 17.80 100 9.40 75 7.50 19.00 50 7.10 18.60 37.5 16.50 25 2.72 6.90 12.10
200 150 100 50 25
Observations with rectangular window at the lagoon inlet
1. W, width of window (mm)
2. b = height of window (mm)
3. A = maximum steady stated wave setup (mm)
4. d, = sill submergence below still water level
5. d2 = soffit submergence below still water level
6. Incident waves for all the measurements reported in Appendix
II were regular waves with a height of 50 mm and a period of
2.2 sec, except where the wave height is stated as 25 or 85
7. Results of wave setup reported are the average values of a
number of tests and the magnitude of setup is for the
maximum steady state condition
Table 2.1: Effect of 25 mm wide window on wave setup; H = 50
mm, T = 2.2 s
Maximum Wave Setup, (mm)
Window Size W, x b
25 x 50 25 x 75 25 x 100
mm mm mm
4.81 4.39 4.39 5.22 6.90 6.90
3.34 2.72 2.51 2.92
3.34 2.72 1.88 3.97
25 x 125
5.22 6.50 6.90 6.90
25 x 25
200 175 150 125 100 75 50
Table 2.2: Effect of 50 mm wide window on wave setup; H = 50
mm, T = 2.2 s
Maximum Wave Setup, An (mm)
50 x 50 50 x 75 50 x 100
mm mm mm
2.51 2.09 2.09
4.18 6.06 7.10
1.25 0.63 0.63
200 175 150 125 100 75
1.04 3.34 4.80 6.48
4.60 5.43 6.50
50 x 125
50 x 25
Table 2.3: Effect of window height of fixed width on wave
setup, sill level fixed at 125 mm. H = 50 mm, T =
Maximum Wave Setup, Al?, with Window Sill at di = 125 mm
W1 = 25 mm W1 = 50 mm W1 = 100 mm d2/d1
b A? b A1 b An mm mm mm mm mm mm
3 6.69 3 6.48 3 0.975
6 6.48 6 5.64 6 0.95
12 6.90 12 4.81 12 0.90 25 6.47 25 3.76 25 1.46 0.80 37 5.85 37 2.51 37 0.70 50 4.80 50 1.67 50 1.25 0.60 62 3.55 62 1.25 62 0.50 75 2.71 75 0.63 75 0.21 0.40 87 2.09 87 87 0.30 100 1.67 100 0 100 0 0.20 112 1.67 112 1.04 112 0.10
125 2.92 125 1.88 125 0.42 0
150 150 2.30 150 -0.20
200 3.34 200 2.30 200 1.88
Table 2.4: Effect of sill submergence and height of 25 mm wide
window; H = 50 mm, T = 2.2 s
Maximum Wave Setup, iW, with 25 mm Wide Window
di = 50 mm di = 125 mm di = 200 mm b Ab b A7 mm mm mm mm mm mm
3 3 6.69 3
6 7.31 6 6.48 6 6.48 12 6.90 12 6.90 12 6.27 25 6.48 25 6.47 25 5.22
37 6.27 37 5.85 37
50 5.22 50 4.80 50 4.81
62 4.50 62 3.55 62
75 5.50 75 2.71 75 4.18
87 87 2.09 87
100 6.90 100 1.67 100 3.34
112 112 1.67 112
125 125 2.92 125 2.92
150 160 3.34 160 200 6.90 200 200
Table 2.5: Effect of sill submergence and height of 50 mm wide
window; H = 50 mm, T = 2.2 s
Maximum Wave Setup, eij, with 50 mm Wide Window
di = 50 mm di = 125 mm di = 200 mm d2/d,
b A7 b A7 b A?
mm mm mm mm mm mm
3 7.31 3 6.48 3 0.975
6 7.31 6 5.64 6 0.95 12 12 4.81 12 6.48 0.90 25 3.55 25 3.76 25 4.18 0.80 37 2.09 37 2.51 37 0.70 50 4.18 50 1.67 50 2.51 0.60 62 62 1.25 62 2.92 0.50 75 5.43 75 0.63 75 2.72 0.40 87 87 87 1.46 0.30 100 6.48 100 0 100 2.09 0.20 112 112 112 0.62 0.10
125 7.10 125 1.88 125 0.42 0
150 150 2.30 150 0 -0.20
200 200 2.30 200 1.04