Wave Height, Setup And Currents Around A Detached Breakwater Submitted To Regular Or Random Wave Forcing

BP 172 X, 38042 Grenoble Cidex 9, France Received 2 1 March 1996; accepted 7 November I996 Abstract Wave height, set-up and currents were measured in the laboratory around a detached

ELSEVIER Coastal Engineering 3 1 (I 997) 77-96

COASTAL ENGINEERING

Wave height, setup and currents around a detached

breakwater submitted to regular or random wave

forcing Mathieu Mory a, Luc Hamm b

a Lahoratoire des Ecoulements G&physiques et Irulusrriels/ IMG, (Laborutoire de I’UJF, de 1’INPG et du

CNRS), BP 53,38041 Grenoble Cklex 9, France

b SOGREAH IngCnie’rie BP 172 X, 38042 Grenoble Cidex 9, France

Received 2 1 March 1996; accepted 7 November I996

Abstract

Wave height, set-up and currents were measured in the laboratory around a detached

breakwater erected on a 1 in 50 plane beach and subjected to regular unidirectional waves, random

unidirectional waves and directional random waves A comparison is made between regular and

random wave cases which had equal incident wave energy While few differences are noticed

between unidirectional and directional random waves, wave height, setup and current variations

are smoother for random waves than for regular waves For regular wave conditions, the location

and the extent of the eddy currents behind the breakwater are strongly constrained by the breaking

line location; a steep gradient of the current is observed across it The circulating flow observed in

the lee of the breakwater surrounds a wide eddy centre with almost quiescent fluid This is

interpreted as a result of the significant reduction of eddy diffusivity outside the surf zone For

comparison with numerical modelling results, an extensive investigation of one regular wave case

was conducted including determination of the vertical structure of the currents It is shown that

currents inshore from the breakwater display limited variations over depth

Keywords: ocean waves; ocean currents; breakwaters; laboratory studies

1 Introduction

Coast and beach protection involves in a number of cases the erection of offshore

breakwaters The diffraction of waves produces eddy currents in the lee of such

breakwaters Waves and currents induce strong morphological changes in their vicinity,

the best known being the appearance of salients and tombolos

037%3839/97/$17.00 Copyright 0 1997 Elsevier Science B.V All rights reserved

PII SO378-3839(96)00053-l

In view of the importance of breakwaters for coastal engineering, the development of numerical modelling for designing them and predicting their impact on coastal morpho- logical changes requires that the results of numerical models be compared to field data

or laboratory experiments This paper presents the results of a laboratory experiment which served as a test experiment in the framework of a research project grouping several European teams involved in numerical modelling All numerical models had basically the same structure: (i) computation of the wave field around the breakwater to estimate the wave driving forces, (ii) computation of the currents generated by the wave forces, (iii) computation of sediment transport and morphological changes The compari- son is limited at the present time to steps (i) and (ii) The experiment was carried out using a concrete solid bottom and sediment transport was excluded The current numerical computations involved either depth integrated (2DH) or fully 3D models The present paper does not discuss the comparison with numerical modelling which is considered elsewhere (Ptchon et al., 1997) It instead focuses on the results of the laboratory experiments

It is well known that wave propagation around a breakwater produces a strong eddy current inshore from the breakwater Special attention was paid in our experiment to the measurement of these eddy currents and their vertical structure, in addition to the measurement of wave height and setup variations in the basin A regular wave case was studied extensively and served for comparison with the numerical modelling However,

a novel feature of the present laboratory study is that it allows some comparison between different wave cases Four incident wave conditions were investigated: two regular wave cases, a unidirectional random wave case and a directional wave case Although the random wave cases were not studied as completely as the reference regular wave case, due to limited time, the incident wave energies were equal for the three cases and this provided an interesting data set for intercomparison On the other hand, the other regular wave case had an incident wave height equal to the equivalent wave height

in the random wave cases

To our knowledge, the first experiments on detached breakwaters were carried out by Gourlay (1974) on a 1 in 10 plane beach and Horikawa and Koizumi (1974) More recent studies were published by Nishimura et al (1985) and Mimura et al (1983) The former paper is mostly concerned with numerical modelling but it includes a comparison with a physical experiment The latter paper is to our knowledge the only one published presenting the results of a laboratory experiment on detached breakwaters that includes sediment transport While all these experiments gave the gross features of the current field in the lee of the breakwater, the published data were not sufficient to evaluate the ability of 2DH or 3D models to compute flow in the vicinity of a breakwater on a mild-sloping beach

2 Experimental methods

2.1 Experimental set-up

Experiments were carried out in the 3D wave basin of the Laboratoire d’Hydraulique

de France (Grenoble) The basin (30 m by 30 m) was equipped on one side with a

M Mary, L Hamm / Coastal Engineering 31 (1997) 77-96

Wave maker

(-0.33)

19

X

-

Fig I Lay-out of experimental set-up

multidirectional wave generator made of 60 paddles Fig 1 shows the lay-out of the experimental set-up The sea bed was a concrete bottom consisting of three parts: (i> a zone (width 4.4 m> of constant depth h = 0.33 m closest to the wave generator, (ii) an underwater plane beach sloping at 1 in 50, (iii) an emerged plane beach sloping at 1 in

20 Considering the symmetry of the flow, half a breakwater 6.66 m long and 0.87 m wide was built perpendicularly to a lateral wall of the basin at a distance of 9.3 m from the still water shoreline and 11.6 m from the mid location of the wave maker The coordinate system referred to in the following is indicated in Fig 1 The OX axis is parallel to the breakwater and the Oy axis is directed toward the wave maker The origin

of the coordinate system is at the comer joining the breakwater to the side wall of the basin The OZ axis is oriented upward z = 0 is the still water level

The breakwater was limited inshore by a vertical wall along which the water depth (at

y = 0) was 0.186 m The offshore side of the breakwater consisted of a 50% sloping beach covered with a 5 cm thick synthetic mattress serving to absorb incident waves For incident regular waves at frequency 0.6 Hz the reflection coefficient of the breakwater beach was found to be 0.19 This coefficient was determined from a directional spectral analysis of the wave signal measured by a directional wave gauge located offshore from the breakwater (x = 4 m, y = - 7.2 m) The analysis was based

on the maximum entropy method proposed by Sand and Mynett (1987) The reflection coefficient was estimated at different frequencies covering the spectrum as the ratio of the wave height density integrated over the directions of wave propagation directed from the breakwater to the wave height density integrated over the directions of wave propagation directed toward the breakwater

80 M Mary, L Hamm / Coastal Engineering 31 (1997) 77-96

Table 1

Incident wave conditions measured offshore ( y = - 7.2 m)

Regular Reg 1 0.075 m

URW

DRW

a Peak period of Jonswap Spectrum

Period 1.69 s 1.69 s 1.69 s a 1.69 s a

The basin was equipped with a travelling bridge parallel to the Oy axis which could

be displaced along the Ox axis Wave gauges, the electromagnetic current meter or the laser doppler anemometry probe attached on the bridge were moved in the area inshore from the breakwater covering the area (0 I x 5 30 m, - 9.3 m I y I 0 m>

2.2 Incident wave conditions

Four incident wave conditions were considered in the course of the study Two regular wave conditions of period T = 1.69 s, referred to in the following as Regl and Reg2, had an incident wave height H,,, = 0.075 m and H,,,,* = 0.117 m, respectively The mean wave height Urn,,_, is the averaged wave height measured from a wave crest to the following trough The propagation of unidirectional random waves toward the breakwater (test case URW in the following) and directional random waves (test case DRW in the following) were also considered Both random wave conditions had a Jonswap spectrum with peak period T = 1.69 s The energy-based significant wave height H,,,, was used for characterizing random wave conditions Table 1 summarizes the incident wave conditions for the four cases The incident wave height values Hm,d

and H,,,, were measured by four gauges placed at y = - 7.2 m (see “Wave height measurements” in the following) They caracterize the “offshore” condition For the two random wave conditions, the energy based rms wave heights H, = H,,/J2 are given in addition to the energy-based significant wave heights H,,,, Table 1 indicates that the results obtained for random wave conditions and those obtained for the regular wave condition Regl provide a comparison between cases having approximately equal wave energy ( H,,,,d = H,,,,) On the other hand, the equivalent wave height HmO in the random wave cases is approximately equal to the mean wave height Hm,d of the regular wave case Reg2 Fig 2 compares the frequency spectra of unidirectional and directional random waves measured offshore They are roughly similar except in the low frequency range where more energy is noticed for the unidirectional wave condition The multidi- rectional random wave condition has a cos2( 0) angular distribution

2.3 Wave height measurements

Wave disturbances were measured using ten capacitive wave gauges and one directional wave gauge includin g an electromagnetic current meter Four capacitive wave gauges located “offshore” ( y = 7 m; x = 4 m, 9 m, 14 m or 19 m) served to

spectral density (m2.s)

0 0.2 0.4 0.6 0.8 1

Frequency (Hz)

1.2 1.4 1.6

waves, - - -: directional random waves

determine the offshore wave conditions and check the direction of wave propagation when necessary Six capacitive wave gauges and the directional wave gauge were attached on the travelling bridge and measured the wave heights simultaneously along a beach profile By displacing the travelling bridge 13 beach profiles were investigated inshore from the breakwater The y locations of two capacitive gauges and of the directional wave gauge were modified for some runs so that wave height variations along each beach line were determined at 9 different y coordinates Fig 3 shows the grid

of wave height measurement locations In the following, the beach profile estimated by

6- offshore -beach line

6-

4-

2- breakwater

shoreline 6

,_

x (m)

averaging the four beach profiles at x = 10 m, 11 m, 12 m and 16 m will be referred to

as the “open beach profile” as the effect of the breakwater becomes very small at this distance from the breakwater as far as wave height or setup are considered This averaged beach profile was introduced as slight differences were noticed when wave height and setup measurements along these four profiles were compared The standart deviations of wave measurements from the averaged open beach values were found to

be at most 17%, 4% and 3% of the averaged value for regular, URW and DRW cases, respectively

The frequency of acquisition of wave data was 20 Hz The recording time was approximately 7 minutes for regular waves (i.e = 240 waves) and 14 minutes for random waves (i.e = 590 waves) For random waves, the wave height records were analysed using spectral analysis and statistical analysis Both approaches were compared

by Hamm (1995) but the results presented here are limited to those determined from the spectral analysis The energy-based significant wave heights H,,,, and the energy based rms wave heights H, = H,,/J2 were determined in the low and high frequency ranges separated by a frequency cut at 0.3 Hz (i.e half the peak frequency) They are respectively denoted H,,,o,,o and H,,,o,hi for the first one and HE,,, and H,,,i for the second one For regular waves, low frequency waves were first removed from the raw signal Their magnitude appeared to be very small; all over the basin H,,,,,,, was less than 2% of Hmo,hi when a spectral analysis of regular waves was performed The mean wave heights H,., were then determined by a wave by wave analysis after removing the zero-crossings of very high frequency parasitic waves (three zero crossing of a wave with period less than 0.6 s) and “parasitic half waves” (two zero crossings separated by

a period less than 0.06 s) Basically, the analysis retains only the primary individual waves so that the number of waves and the mean period determined at different locations along the open beach profile remain constant Details on the procedure are given by Hamm (1995)

2.4 Set-up measurements

The mean water levels were determined by measuring the mean piezometric levels using tappings (designed following Battjes and Janssen, 1978) in the sea bed connected

to stilling wells in which the water level is determined by an ultrasonic probe of 0.2 mm accuracy The acquisition frequency was 1 Hz and the recording times were the same as for wave height measurements The locations of the piezometric tappings are also included in Fig 3 Five beach lines with 7 tappings were investigated The tappings closest to the still water shoreline were flush in a narrow slot 1 cm wide and 10 cm deep below the mean water level in order to eliminate the systematic errors made if the tapping becomes dry

2.5 Current measurements

Current measurements were obtained using a two components TSI Laser Doppler Anemometer (LDA) and an Electromagnetic Current Meter (EMC) installed on the directional wave gauge The EMC is 40 mm in diameter and 18 mm thick

M Mary, L Hmnm / Coasral Engineering 31 (1997) 77-96 83

The LDA device uses an immersed probe mounted on an optic fiber operating in backscattering mode The probe is a cylinder 15 cm long, 1.2 cm in diameter, and its focal length is 80 mm in water The horizontal current velocity field was investigated with this probe for one regular wave case only (Regl) in the area (1 m I x I 10 m, - 6

m I y I - 1 m> behind the breakwater with a mesh of 1 m between grid points The two horizontal velocity components u and u were measured at mid-depth at each grid point Detailed vertical profiles (2 cm above the bottom to 2 cm below the still water level with a mesh of 1 cm> of the two velocity components were also measured using LDA at

10 locations for which it appeared of importance for numerical modelling to estimate the variations over the vertical Special attention was paid to the vicinity and the head of the breakwater as well as to vertical profile measurements in the breaking zone

The rate of velocity measurements obtained in time was usually in the range 20 data/s to 300 data/s Velocity measurements were digitized using even-time sampling

at 50 Hz frequency (85 data cover one wave period) The mean velocity was deduced by averaging the velocity records in time A recording time of 3 minutes 25 s was usually sufficient to obtain mean velocity variations from different records below lo%, except around the eddy centre where the current is very small Moreover, the recording time was doubled (6 minutes 50 s) when the measurement point was located in the breaking zone

The signal from the electromagnetic current meter installed on the directional wave gauge was also analysed to get the current at about mid-depth Two lines inshore from the breakwater were investigated for the four wave cases The first line (1 m 5; x I 16 m; y = - 0.32 m) is in the lee of the breakwater while the second (1 m I x I 16 m;

y = - 5.6 m) is partly located in the breaking zone

2.6 Visualisations

A squared grid (1 m by 1 m> was painted on the sea bottom The flow was visualised using a camera placed above the surf zone and pointing vertically downwards The camera was moved to four positions to cover the whole width of the basin For regular wave conditions, the visualisations were analysed quantitatively to determine the position of the breaking line Tracking of dye clouds was also employed to visualise the general current circulation Dye lines were injected at several locations and the displace- ments in time of the dye clouds were determined quantitatively by analysing sets of pictures taken with a time interval of 4 s The visualisations appeared to be a fruitful tool for comparison between regular and random wave conditions

3 Wave height and set-up patterns

Fig 4a shows a general view of the facility operating with unidirectional random wave (URW) conditions The photograph in Fig 4b shows the wave pattern observed for regular waves (Regl) The picture focuses on the region behind the breakwater and

on the surf zone Due to diffraction, wave activity is much reduced in the lee of the

Fig 4 (a) General view of the facility and unidirectional random wave pattern (URW) (b) Wave pattern in the surf zone for regular wave conditions (Regl)

breakwater The breaking line on the open beach (X 2 8 m) is observed to be around y= -4m

As mentioned in Section 2, the energy of incident regular waves Regl is approxi- mately equal to the mean energy of the random wave conditions This implies that the highest waves for random conditions are significantly higher than regular waves

M Mary, L Hamm / Coastal Engineering 31 (1997) 77-96 85

Accordingly, it can be seen in Fig 4a that some waves are breaking when they pass across the line x = 0 of the breakwater alignment

Fig 5a compares the changes in wave height on the open beach, where the alongshore variation is small, for the regular wave case Regl and the two random wave cases The mean wave height H,,,d

H

and the energy based rms wave heights HE+ and E,lo are plotted in Fig 5a, respectively for the regular and random wave conditions

The three wave cases have equal energy offshore as confirmed by the data points at

y = 7 m It is verified that regular waves break around the position y = - 4 m The wave profiles are much smoother for random waves; a slight decrease in wave height is already noticeable at the position x = 0 The changes in wave height on the open beach are similar for undirectional random waves and directional random waves but low frequency waves are significantly higher for unidirectional random waves than for directional random waves The decrease in high frequency wave height is satisfactorily modelled by the Battjes and Janssen (1978) prediction, which is superimposed on the graph The comparison with Battjes and Janssen’s prediction is actually made by comparing the model prediction with the variation of H,,,i whereas Battjes and Janssen

originally considered the full spectrum Hamm (1995) pointed out that Battjes and Janssen model overestimates dissipation near the shoreline when low frequency waves are not removed from the computation of H, This overestimation appeared also in the comparison made by Battjes and Stive (1985) (Fig 4) although they did not paid much attention to it This is the reason why Hahi and HE,,o are used in the present study Fig

5b presents the changes in set-up on the open beach for the three conditions They are in qualitative agreement with what is commonly expected but the Battjes and Janssen (1978) prediction is not accurate, presumably because the roller effect is not taken into account (Hamm, 1995) It can be seen again that the changes in setup are smoother for random waves

Fig 5c compares the high frequency changes in wave height on the open beach for the regular wave case Reg2 and the two random wave cases The energy-based significant wave height H,,,o,hi is used to represent the results for random waves as an

equivalent wave height It decays in the surf zone in a similar manner to the wave height

of the regular wave test Reg2

Wave height contour plots and set-up contour plots are superimposed in Fig 6a to d for the four wave conditions Regl, UNR, DRW and Reg2 The mean wave height Hm,d

is used for regular wave cases whereas the energy-based rms wave height Hmo,hi is used

to represent the results for random waves Fig 6a to c thus compare regular and random wave conditions having equal energy As expected, the regular wave case Reg2 (Fig 6d) displays greater wave heights The wave height and set-up contour plots are satisfacto- rily consistent For regular waves (Fig 6a and d) the set-up gradient is clearly related to the significant wave height fall inshore from the breaking line in the surf zone For the lower energy regular wave case Regl, it is particularly significant that the set-up contours curve when approaching the breakwater and remain parallel to the breaking line Behind the breakwater the wave height is significantly reduced by the effect of diffraction but this is not linked to significant set-up variations For the higher energy regular wave case Reg2, the breaking line is directed perpendicularly to the breakwater inshore from it On the open beach (x > 6.6 m) the breaking line is shown in Fig 6d as

86 M Moty, L Hamm/ Coastal Engineering 31 (1997) 77-96

wave heights (m)

0.12

b

0.1

0.08

0.06

0.04

0.02

n

-. -+ -+-mm

,

~ &*_4 * - ~

"-10 -a -6 -4 -2 0 2 4 6

distance (m) set-up (m)

a

0.015

b

t

-O.OlL' ’ ’ ’ I ! ’ I I /

distance (m) wave heights (m)

V I_

0.12

0.1

0.06

0.06

0.04

0.02

-I

-10 -a -6 -4 -2 0 2 4 6 8

distance (m)