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

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COASTAL ENGINEERING ELSEVIER Coastal Engineering (I 997) 77-96 Wave height, setup and currents around a detached breakwater submitted to regular or random wave forcing Mathieu Mory a, Luc Hamm b aLahoratoire 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 March 1996; accepted November I996 Abstract Wave height, set-up and currents were measured in the laboratory around a detached breakwater erected on a 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 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 PII SO378-3839(96)00053-l 1997 Elsevier Science B.V All rights reserved 78 M Mary, L Humm/ Cmxtul Engineering 31 (1997) 77-96 In view of the importance of breakwaters for coastal engineering, the development of numerical modelling for designing them and predicting their impact on coastal morphological 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 comparison 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 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 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 19 maker (-0.33) X - Fig I Lay-out of experimental set-up multidirectional wave generator made of 60 paddles Fig 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 in 50, (iii) an emerged plane beach sloping at 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 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 = 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 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 = 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 Incident wave conditions measured Wave type H m.d Regular Reg Regular Reg2 URW DRW 0.075 m 0.117 m a Peak period of Jonswap offshore ( y = - 7.2 m) H mo 0.115 m 0.115 m H, = Hm /J2 Period 0.081 m 0.081 m 1.69 s 1.69 s 1.69s a 1.69 s a Spectrum 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 30 m, - 9.3 m I y I 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 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 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 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 multidirectional 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 = m; x = m, m, 14 m or 19 m) served to hf Mary, L Hamm / Coastal Engineering 31(1997) 81 77-96 spectral density (m2.s) 0.2 0.4 0.8 0.6 1.4 1.2 1.6 Frequency (Hz) Fig Frequency spectrum of incident waves measured offshore ( y = 7.3 m) : waves, - - -: directional random waves Unidirectional random 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 different y coordinates Fig shows the grid of wave height measurement locations In the following, the beach profile estimated by 6- offshore -beach c line + + + 642z r breakwater IJ + ‘1 + b+ ++ o+ -8 + + b+ + + +o+ + ,_ foe + foC + + ts + e + to+ f %b+ + +o+ + + shoreline 10 15 20 x (m) Fig Locations tappings of wave height and set-up measurements in basin: +, wave gauges; 0, piezometric 82 M Mary, L Humm / Coustul Engineering 31 (1997) 77-96 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 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 Hz and the recording times were the same as for wave height measurements The locations of the piezometric tappings are also included in Fig Five beach lines with tappings were investigated The tappings closest to the still water shoreline were flush in a narrow slot 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, - m I y I - m> behind the breakwater with a mesh of 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 cm below the still water level with a mesh of 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 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 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 displacements in time of the dye clouds were determined quantitatively by analysing sets of pictures taken with a time interval of s The visualisations appeared to be a fruitful tool for comparison between regular and random wave conditions 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 84 M Mary, L Hamm / Coasrul Engineering Fig (a) General view of the facility and unidirectional surf zone for regular wave conditions (Regl) 31 (1997) 77-96 random wave pattern (URW) (b) Wave pattern in the breakwater The breaking line on the open beach (X m) is observed to be around y= -4m As mentioned in Section 2, the energy of incident regular waves Regl is approximately 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 = 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 and the energy based rms wave heights HE+ and H 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 = m It is verified that regular waves break around the position y = - m The wave profiles are much smoother for random waves; a slight decrease in wave height is already noticeable at the position x = 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 satisfactorily 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 significant that the set-up lower energy regular wave case Regl, it is particularly 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 M Moty, L Hamm/ Coastal Engineering 31 (1997) 77-96 86 wave heights (m) 0.12 b 0.1 0.08 0.06 0.04 -. -+ -+-mm 0.02 , ~ &*_4 * - ~ n "-10 -a -6 -4 -2 distance a (m) set-up (m) 0.015 b t -O.OlL' ’ -10 -9 wave heights V ’ -a ’ -7 I ! -6 -5 distance (m) ’ I I / -4 -3 -2 -1 (m) I_ 0.12 0.1 0.06 0.06 0.04 0.02 -I -10 -a -6 -4 -2 distance (m) M Mary, L Hamm / Coastal Engineering 31 (1997) 77-96 87 (4 0.02 I I x (m) 10 12 IO 12 (b) 0.03 - I I 6 x Cm) Fig Wave wave height indicated by Reg2 Wave height ( -, units: m) and set-up (- - -, units: mm) contour plots lo-* m and mm between and set-up contour lines, respectively (a) Regl Wave height value is H,,,d The breaking line is - - - (b) URW Wave height value is H,,,o,h, (c) DRW Wave height value is H,,,u.hl cd) height value is H,,,,* The breaking line is indicated by - - - Fig Changes H~.~ URW: Janssen’s (1978) -_O URW: - q -9 &a,,,, in wave height and set-up on the open beach (a) Changes in wave height Regl: O-_, -, HE,hi; -w -, HE ,“ DRW: - - A , HE,hi; A , H,,,, Battjes and prediction of random wave decay is superimposed, - .- .: (b) changes in set-up Regl: - q -, DRW: a , (c) Changes in wave height Reg2: -0 , H,,,d URW: DRW: - - A - -, H,,,O,hi M Moty, L Hamm/ 88 -lO- Coastal Engineering 31 (1997) 77-96 \ -_ - -P x Cm) ,4 '\*5 10 12 \yy/, - -_ -=a (d) 0” -_ 0.09 _ - _-_ (I, , r,,/,,11, _ , r,,,I,,/, - r' _ ,, - 0.07 - 0.05 -i -_ -lOI -+7 t \ ~\ \ \ '+6 '+6 ', , \ ‘._ ' ‘.+6 '\ \ I x (W 10 12 Fig (continued) the straight line y = It was actually not clearly visible in the visualisation pictures, but the line y = is certainly close to the real location of the breaking line Similar wave height and set-up patterns are measured for the random wave cases URW and DRW (Fig 6b and cl The wave activity is slightly greater in the lee of the breakwater for directional random waves than for unidirectional waves, as expected The contours are again observed to be much smoother for random waves as compared to regular waves because waves break at different depths M Mary, L Hamm/ Coasral Engineering 31 (1997) 77-96 89 Current measurements Because current measurements take a very long time, it was decided to carry out LDA measurements only for the regular wave case Regl so that a full set of data, including vertical profiles of current, could be obtained for these conditions A limited comparison of velocity measurements for regular and random wave conditions was nevertheless available from the EMC data set Fig shows the eddy pattern measured behind the breakwater for the low energy regular wave case Regl The measurements were obtained at mid-depth, but they are physically meaningful data because the flow displays only limited variations over the vertical, as discussed later The eddy structure produces strong jet-like flows of up to 0.25 m/s along the lateral wall toward the breakwater and along the breakwater toward the open beach EMC velocity data are also included in Fig Good consistency between LDA and EMC velocity measurements is obtained Superimposed in Fig are the breaking line and the set-up contour plots shown previously in Fig 6a A striking feature is the observation that the breaking line between m I x I m is a limiting line between the strong currents in the surf zone and a wide eddy centre with almost quiescent fluid It is worth noting that the breaking line, the set-up contours and the velocity vectors are curved and roughly parallel in this region Unfortunately, current measurements could not be made very close to the shore line ( y < - m> because the probe is too large compared to the water depth (which is less that 6.6 cm) The domain (0 I x I m; - 10 m < y I - m) inshore from the breakwater displays a complicated -6 ,- a 10 x (m) Fig Currents measured EMC measurements , at mid-depth for regular wave conditions Regl + set-up contour lines superimposed; - - -, breaking , LDA measurements; line -O+, 90 M Mot-y, L Humm/ Cou.std Engineering 31 (1997) 77-96 wave propagation pattern because waves arriving obliquely on the beach are reflected by it Some of the reflected waves break The breaking line was therefore not prolonged in this area, which actually appears as a region where multiple breaking events occur Significant set-up contour gradients are observed in the vicinity of the lateral wall Orders of magnitude of the set-up gradients and of the curvature of the set-up contours provide consistent estimates of the pressure gradients required to make the current turn when approaching the lateral wall inshore and in the vicinity of the corner joining the lateral wall and the breakwater Another striking feature is the observation of a wide quiescent region in the centre of the eddy The eddy centre is far from being in solid body rotation Unexpected contour gradients are noticed in the eddy centre where no current is measured Their origin is not clearly understood Nothing wrong could be found in the measurement procedure but Fig 6a also shows distorted wave height contour lines in this area Our interpretation of Fig is that the eddy flow is driven by the wave breaking in the surf zone Currents are produced in the surf zone and then proceed in an eddy-like structure The set-up gradients mainly adjust to produce the pressure gradients required for the eddy current to rotate For this low-energy regular wave case Regl, the breaking line is located well inshore and far from the breakwater A wide eddy centre with almost quiescent fluid is observed because eddy diffusivity is low over a large area behind the breakwater Eddy diffusivity is commonly scaled by the turbulent kinetic energy k and the turbulent lengthscale (E = 1Jk) As the turbulent kinetic energy decreases rapidly outside the surf zone we presume that setting up solid body rotation inside the eddy core takes a very long time because eddy diffusivity is small there and momentum diffuses very slowly toward the eddy centre The velocity data presented in Fi g were checked with regard to mass conservation Computing the mass fluxes for each square element with a velocity measurement at each of the four corners revealed that the eddy flow plotted satisfactorily conserves mass, -2 m> On the one hand, except in the domain (8 m I x 10 m; -4 rnlyl measurement errors were examined They could unfortunately not be proved because the LDA was nolonger available when this defect in mass conservation was noticed On the other hand, it is worth remarking that this area contains the breaking line As shown later, significant variations in the current over the vertical are observed there, implying that current measurements made at mid-depth are not accurate estimates of currents averaged over the vertical in the vicinity of the breaking line Computing mass conservation across lines y = - m, y = - m and y = - m with x I 10 m also provides insight into the general circulation inside the tank A net flux is actually obtained directed shorewards This implies that the flow arriving on the beach between x = m and x = 10 m is partly recirculated in the basin by an alongshore current directed toward the lateral wall at x = 30 m This was verified from dye line displacements as discussed later Vertical profiles of the two horizontal current components measured using LDA at several positions in the basin are shown in Fi,.0 Fig Sa presents three velocity profiles in the lee of the breakwater ( y = - m) as well as one profile measured very close to the head of the breakwater (X = m, y = -0.06 m, profile N) In the lee of the breakwater the current does not much vary over the vertical except in the vicinity of the lateral wall where the flow turns (profile A) A rapid rotation of the flow direction M Mary, L Hamm / Coastal Engineering 31 (1997) 77-96 Fig Vertical velocity profiles measured at various locations for regular waves (Regl) (a) Vertical profiles of currents measured in the lee of the breakwater : Prof A (x = m, y = - m, h = 0.166 m); W : Prof B (x=3m, y=-1 m, h=O.l66m); 0: prof.C(x=7m,y=-lm,h=0.l66m);O:prof.N(x=7m, y = -0.06 m, h = 0.185 m) (b) Vertical profiles of currents at about mid-distance between the breakwater and theshoreline.~:prof.D(x=lm,y=-3m,h=0.126m~;0:prof.E~x=3m,y=-3m,h=O.l26m~; ~:prof.F(x=l0m,y=-4m,h=0.106m);~:prof.I~x=l5m,y=-5m,h=0.086m~;A:prof.G m,y=-6m,h=0.066m);r:prof.H(x=4m,y=-6m,h=0.066m) (x=1 toward the shoreline is observed when the current runs past the head of the breakwater (profile C> Only limited 3D effects are noticed on the vertical profile measured near the head (profile N) Fig 8b presents six profiles measured at different y locations but all of them being around the mid distance between the breakwater and the shoreline The main velocity component is the cross-shore velocity component along the lateral wall (profile D) while the fluid is at rest over the whole layer depth in the eddy centre (profile E) Profiles F and I were measured in the surf zone While the vertical velocity variations are small for profile F, they are significant on the vertical profile of the cross-shore component on the open beach (profile I> due to the fact that breaking waves have 92 M Mm-y, L Hamm / Coastal Engineering 31 (1997) 77-96 unidirectional propagation on the open beach The alongshore velocity component u is of the order of 0.08 m/s on the open beach and directed toward the lateral wall opposite the one along the breakwater as mentioned before Profiles G and H measured closer to the shoreline confirm that the flow varies very little over depth Altogether, the vertical velocity profiles support the conclusion that the flow is approximately two-dimensional in the regions of strong currents behind the breakwater but that 3D effects cannot be neglected in the surf zone on the open beach Dye line displacements are displayed in Fig 9a to d for the four wave conditions by drawing the locations and shapes of dye line pairs observed at a time interval of 6t The initial dye lines are drawn in solid line while the subsequent positions and shapes of these dye lines are represented as dashed lines when 6t = s and as dotted lines when 6t = s For the two regular wave cases (Fig 9a and d) the breaking line is also plotted For the high energy regular wave case Reg2, waves break when they pass across the line of alignment of the breakwater Breaking occurs nearly uniformly around the line y = because the waves have not yet been submitted to diffraction; the breaking line is prolonged perpendicularly inshore from the breakwater over a distance of about m before diffraction becomes visible Fig 9d and a indicate that the domain behind the breakwater, where no wave breaking occurs, is only slightly limited for the high energy regular wave case as compared to the low energy regular wave case Accordingly, a wide eddy centre with almost no mean current is also noticed on the left of the breaking line for the high energy regular wave case (Fig 9d) as shown by the very small dye line displacements observed The difference between regular and random waves in the eddy structure behind the breakwater is clearly shown when comparing Fig 9a and d to Fig 9b and c Rotation is clearly visible within the eddy core for the random wave cases while the eddy current surrounds a region of quiescent fluid for the two regular wave cases Since currents are mainly produced by the breaking of waves, their spatial distribution is smoother for random waves because breaking events are distributed over a wider area On the other hand, the breaking line location is not submitted to time variations for regular waves so that large variations of the current magnitude should be expected across the breaking line Fig provides additional insight into the general circulation inside the tank and longshore currents on the open beach except for the high energy regular wave case Reg2 Dye line displacements in the surf zone on the open beach could not be quantitatively interpreted for this case and are not shown in Fig 9d Longshore currents are observed on the open beach, carrying some fluid away from the breakwater A reversal of the longshore current occurs around the line x = 20 m for Regl and URW (Fig 9a and b) cases, which indicates the existence of a rip current For the regular wave case Regl, the longshore current is directed away from the breakwater from x = 11 m to x = 16 m, in agreement with the Laser Doppler measurements made at x = 16 m (Fig 8b) This observation contradicts the observations of Nishimura et al (1985) who reported a longshore current directed in the opposite direction However, this is a minor point of disagreement as the velocities in the longshore currents, of the order of a few cm/s, are much weaker than the velocities in the eddy structure behind the breakwater Longshore profiles of the current magnitude in the lee of the breakwater at y = - 0.32 m measured for the four wave conditions usin g an Electromagnetic Current Meter M Mary, L Hamm/ Coastal Engineering 31 (1997) 77-96 93 (4 -10' I 10 15 20 25 x (m) 03 I -10 b 10 , 15 I 20 25 I -10 I 10 15 20 25 x (m) (4 ( Fig Dye line displacements inshore from the breakwater and in the surf zone on the open beach Solid lines represent the initial locations of dye lines The dye line location at the subsequent time interval is plotted as a dashed line when i3r = s and as a dotted line when 6r = s (a) Regular waves Regl The breaking line is indicated by - - - (b) Unidirectional random waves (c) Directional random waves Cd) Regular waves Reg2 The breaking line is indicated by - - - M Mary, L Humm / Coustal Engineering 94 31 (1997) 77-96 velocity speed (m/s) 0.4 0 6 distance 10 12 14 16 (m) Fig 10 Velocity magnitude in the lee of the breakwater ( y = - 0.32 m) measured by EMC Comparison between regular waves (-0 , Regl) (-• , Reg2), unidirectional random waves (0 - ) and directional random waves ( - - A - -1 provide an additional quantitative basis to the former observations They are shown in Fig 10 Firstly, it may be noticed that the current is stronger in the lee of the breakwater for the high energy regular wave case Reg2 than for the low energy regular wave case Regl Regl, URW and DRW cases have equal initial wave energy and Fig 10 shows that the currents are weaker for the random wave conditions than for the regular wave condition Regl This is consistent with the conclusion of Section 3, according to which wave height and set-up variations are smoother for random waves Finally, it can again be deduced from Fig 10 that unidirectional random waves and directional random waves are very similar Conclusions The flow features observed by the previous laboratory studies and computed by various numerical models in the vicinity of a breakwater were qualitatively recovered in our experiment, in particular the significant reduction of wave activity and the strong eddy current in the lee of the breakwater The detailed measurements of the current field made in our experiment for regular incident waves show that the breaking line severely constraints the kinematics in the eddy structure The breaking line has a constant location when the basin is submitted to regular wave propagation and a steep gradient of the current is observed across this line For the two regular wave cases studied in this paper, the area limited by the breakwater and the breaking line was fairly large and the eddy current surrounded a wide region of fluid at rest This feature was not visible in the experimental results presented by Nishimura et al (1985) due to a lack of data obtained inside the eddy core The existence of a vortex core at rest can be explained by considering that eddy diffusivity presumably decreases rapidly outside the surf zone so that setting up solid body rotation in the central core takes a very long time A quite M Mary, L Hamm / Coastal Engineering 31 (1997) 77-96 95 different eddy pattern is observed for random wave conditions: the currents are much less concentrated because breaking events are much more distributed in space and currents are generated over a wider area Since the eddy diffusivity is presumably also more homogeneous in space, rotation of the eddy centre for random waves is more like solid body rotation Our experiment allowed a quantitative comparison between regular waves, unidirectional random waves and directional random waves because the conditions were chosen so that the incident wave energies were the same for the three cases Large differences were noticed The wave patterns and set-up displacements are much smoother and the currents much less concentrated for random waves More surprisingly, few differences were observed between unidirectional and directional random waves Wave height levels in the lee of the breakwater are slightly higher for directional random waves than for unidirectional random waves On the other hand higher low frequency waves are produced on the open beach for unidirectional random waves than for directional random waves The experiment was primarily intended to serve as a test experiment for the validation and comparison of numerical models of different kinds, either depth-integrated or three-dimensional The comparison of our experimental results with numerical computations performed for the same geometry and the same incident wave conditions is considered in detail by Pe’chon et al (1997) Nevertheless, two general recommendations with regard to numerical modelling can still be drawn from our experiment The first is that depth-integrated numerical models should satisfactorily compute current fields because only limited variations in current fields over depth were measured in the laboratory The second point stressed by the experiment is the importance for numerical modelling of accurate prediction of the breaking line location and of appropriate parameterisation of eddy diffusivity variations inside and outside the surf zone Although most numerical computations of currents are qualitatively in agreement with observations in the laboratory, the quantitative discrepancies might be more critical when considering the further step of sediment transport around a breakwater Acknowledgements This work was carried out as part of the G8 Coastal Morphodynamics Programme, which is funded partly by the Service Technique des Ports Maritimes et des Voies Navigables (France), Minis&e de l’Equipement, des Transports et du Tourisme (France) and the European Commission (contract MAS2-CT92-0027) References Battjes, J.P and Janssen, F.M., 1978 Energy loss and set-up due to breaking of random waves In: Proc 16th Int Conf on Coastal Engineering, Hamburg Battjes, J.P and Stive, M.J.F., 1985 Calibration waves J Geophys Res., 9o(C5): 9159-9167 AXE, pp 569-587 and verification of a dissipation model for random breaking 96 M Mary L Humm / Coustul Engineering 31 (1997) 77-96 Gourlay, M.R., 1974 Wave set-up and wave generated currents in the lee of a breakwater or headland In: Proceedings 14th Int Conf on Coastal Engineerin g, Copenhagen AXE, pp 197661987 Hamm, L., 1995 Modtlisation numerique bidimensionnelle de la propagation de la home dans la zone de dtferlement Ph.D Thesis, Univ .I Fourier, Grenoble Hotikawa, K and Koizumi, C., 1974 An experimental study on the function of an offshore breakwater In: Proc 29th Annual Conference, Japanese Society of Civil Engineers, pp 85-87 Mimura, N., Shimizu, T and Hotikawa, K., 1983 Laboratory study on the influence of detached breakwater on coastal change In: Proc Coastal Structures’83 ASCE, pp 740-752 Nishimura, H., Maruyama, K and Sakurai, T., 1985 On the numerical computation of nearshore currents In: Coastal Eng Jpn., 28: 137- 145 Ptchon, P., Rivero, F., Johnson, H., Chesher, T., O’Connor, B., Tanguy, J.M., Karambas, T., Mory, M and Hamm, L., 1997 Intercomparison of wave-driven current models Coastal Eng., submitted Sand, S.E and Mynett, A.E., 1987 Directional wave generation and analysis In: Proc IAHR Seminar on Wave Analysis and Generation in Laboratory Basins, Lausanne, pp 209-235
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