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

COASTAL
ENGINEERING
ELSEVIER

Coastal Engineering

3 1 (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 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
PII SO378-3839(96)00053-l

0 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 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

19

maker

(-0.33)

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

Wave type

H m.d

Regular Reg 1
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 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 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 = 7 m; x = 4 m, 9 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

0.4

0.8

0.6

1

1.4

1.2

1.6

Frequency (Hz)

Fig. 2. 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 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
c

line
+

+

+

642z
r

breakwater

IJ
+
‘1

+ b+

++

o+

-8

+

+ b+

+

+ +o+
+

,_

0

foe

5

+ foC

+

+

ts

+

e

+

to+

f

%b+ +

+o+

+ +

6

shoreline

10

15

20

x (m)
Fig. 3. 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
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 displacements 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


84

M. Mary, L. Hamm / Coasrul Engineering

Fig. 4. (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 2 8 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 = 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 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 = 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 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

0

distance

2

4

a

6

(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

0

(m)

I_

0.12
0.1
0.06
0.06
0.04
0.02

-I

-10

-a

-6

-4

-2

distance

0

(m)

2

4

6

8


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

87

(4
0.02

I

I

0

2

4

6
x (m)

6

10

12

IO

12

(b)

0.03 -

I

I

0

2

4

6

6

x Cm)

Fig. 6. Wave
wave height
indicated by
Reg2. Wave

height (---,
units: m) and set-up (- - -, units: mm) contour plots. lo-* m and 1 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. 5. 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-_,
0 ---, 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

0

2

6

x Cm)

4

6

.
. ,4

'\*5

10

12

\yy/,---.
-_
-=a

(d)
0”

-_

1

0.09

--_

---__

_-_
(I,
,--r,,/,,11,
_----,
--. r,,,I,,/,---__--r' _
,,

-

0.07

-

0.05

-i

.
-_

-lOI
---+7
t
0

\

2

~\
\

\

'+6

'+6

', ,

\

‘._

'.
‘.+6

'\

\
I

4

6
x (W

6

10

12

Fig. 6 (continued).

the straight line y = 0. It was actually not clearly visible in the visualisation pictures, but
the line y = 0 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

4. 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. 7 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. 7. Good consistency
between LDA and EMC velocity measurements is obtained. Superimposed in Fig. 7 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 5 m I x I 9 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 < - 6 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 5 m; - 10 m < y I - 6 m) inshore from the breakwater displays a complicated

-6

,-

0

2

4

6

a

10

x (m)

Fig. 7. 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. 7 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 1 (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. 7 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 5 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 = - 2 m, y = - 3 m and y = - 4 m
with 0 5 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 = 8 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 8. Fig. Sa presents three velocity profiles
in the lee of the breakwater ( y = - 1 m) as well as one profile measured very close to
the head of the breakwater (X = 7 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

3
Fig. 8. Vertical velocity profiles measured at various locations for regular waves (Regl). (a) Vertical profiles

of currents measured in the lee of the breakwater. 0 : Prof. A (x = 1 m, y = - 1 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 = 8 s and as dotted lines when
6t = 4 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 = 0
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 3 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. 9 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'
0

I

5

10

15

20

25

x (m)

03

I

1

-10

b.
0

5

10

,
15

I
20

25

I

-10 0

I

5

10

15

20

25

x (m)
(4

(

Fig. 9. 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 = 8 s and as a dotted line when 6r = 4 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
0

2

4

6

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.

5. 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
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AXE, pp. 569-587.
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96

M. Mary. L. Humm / Coustul Engineering

31 (1997) 77-96

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