RESEARCH ARTICLE
10.1002/2016JC012072
Large-scale laboratory study of breaking wave hydrodynamics
over a fixed bar
Dominic A. van der A
1
, Joep van der Zanden
1,2
, Tom O’Donoghue
1
, David Hurther
3
,
Iv
an C
aceres
4
, Stuart J. McLelland
5
, and Jan S. Ribberink
2
1
School of Engineering, University of Aberdeen, Aberdeen, UK,
2
Department of Water Engineering and Management,
University of Twente, Enschede, Netherlands,
3
Laboratoire des Ecoulements G
eophysiques et Industriels, CNRS, University
of Grenoble Alpes, Grenoble, France,
4
Laboratori d’Enginyeria Mar
ıtima, Universitat Polite
`
cnica de Catalunya, Barcelona,
Spain,
5
Department of Geography, Environment and Earth Sciences, University of Hull, Hull, UK
Abstract A large-scale wave flume experiment has been carried out involving a T 5 4 s regular wave
with H 5 0.85 m wave height plunging over a fixed barred beach profile. Velocity profiles were measured at
12 locations along the breaker bar using LDA and ADV. A strong undertow is generated reaching
magnitudes of 0.8 m/s on the shoreward side of the breaker bar. A circulation pattern occurs between the
breaking area and the inner surf zone. Time-averaged turbulent kinetic energy (TKE) is largest in the
breaking area on the shoreward side of the bar where the plunging jet penetrates the water column. At this
location, and on the bar crest, TKE generated at the water surface in the breaking process reaches the
bottom boundary layer. In the breaking area, TKE does not reduce to zero within a wave cycle which leads
to a high level of ‘‘residual’’ turbulence and therefore lower temporal variation in TKE compared to previous
studies of breaking waves on plane beach slopes. It is argued that this residual turbulence results from the
breaker bar-trough geometry, which enables larger length scales and time scales of breaking-generated
vortices and which enhances turbulence production within the water column compared to plane beaches.
Transport of TKE is dominated by the undertow-related flux, whereas the wave-related and turbulent fluxes
are approximately an order of magnitude smaller. Turbulence production and dissipation are largest in the
breaker zone and of similar magnitude, but in the shoaling zone and inner surf zone production is
negligible and dissipation dominates.
1. Introduction
Van Rijn et al. [2013] identified the surf zone as an important area where our understanding and predictive
capability of sediment transport remains poor. In particular, suspended sediment dynamics around the
breaker bar in the outer surf zone, near-bed sediment dynamics in the wave boundary layer under breaking
waves, vertical structure of sediment dynamics in the inner surf zone, and coherent flow structures and
intermittent sediment stirring under breaking waves were highlighted as important topics for future
research. Improving this understanding of the sediment dynamics throughout the surf zone requires a
detailed knowledge of the intrawave hydrodynamics and turbulence structure under breaking waves.
Field measurements have provided valuable insights into the effects of wave breaking on hydrodynamics.
In the surf zone, wave energy dissipation and roller formation affect the main terms in the cross-shore
momentum balance, leading to time-averaged velocities that are strongly nonuniform in the cross-shore
direction [Garcez Faria et al., 2000]. Field studies have also revealed that wave breaking is an important
mechanism of turbulence production [Thornton, 1979]. A significant part of breaking-induced turbulence is
dissipated above trough level [Grasso et al., 2012], while the remainder spreads through the water column,
leading to increased magnitudes of Reynolds shear stress and turbulent kinetic energy through the com-
plete water column [Ruessink , 2010]. Turbulence dissipation rates decrease with distance from the free sur-
face [George et al., 1994; Feddersen et al., 2007], which indicates that wave breaking is the dominant source
of turbulence dissipation [Grasso et al., 2012].
These field studies generally cover a limited number of cross-shore and vertical measurement locations,
and the irregularity and alongshore-nonuniformity of the wave limits detailed investigation of the temporal
Key Points:
High spatial and temporal resolution
velocity measurements around a
large-scale breaker bar
Relatively high residual turbulence
compared to wave breaking on a
plane slope
Horizontal and vertical transport of
TKE is primarily advective and
dominated by the time-averaged
velocities
Correspondence to:
D. A. van der A,
d.a.vandera@abdn.ac.uk
Citation:
van der A, D. A., J. van der Zanden,
T. O’Donoghue, D. Hurther, I. C
aceres,
S. J. McLe lland, and J. S. Ribberink
(2017), Large-scale laboratory study of
breaking wave hydrodynamics over a
fixed bar, J. Geophys. Res. Oceans, 122,
3287–3310, doi:10.1002/
2016JC012072.
Received 18 JUN 2016
Accepted 16 MAR 2017
Accepted article online 20 MAR 2017
Published online 24 APR 2017
V
C
2017. The Authors.
This is an open access article under the
terms of the Creative Commons Attri-
bution License, which permits use, dis-
tribution and reproduction in any
medium, provided the original work is
properly cited.
van der A ET AL. BREAKING WAVE HYDRODYNAMICS 3287
Journal of Geophysical Research: Oceans
PUBLICATIONS
and spatial variation in the hydrodynamics. Consequently, much of our existing knowledge on breaking
wave hydrodynamics comes from small-scale laboratory experiments, the most detailed of which are con-
ducted in wave flumes involving fixed, nonmobile beach profiles. Fixed profiles avoid practical complica-
tions associated with moving bed levels, and allow the use of high-resolution optical and nonintrusive
measurement techniques. Numerous small-scale experiments studied plunging or spilling waves over hori-
zontal [Chang and Liu, 1999; Drazen and Melville, 2009] or plane sloping bed profiles [Okayasu et al., 1986;
Nadaoka et al., 1989; Ting and Kirby, 1994, 1995, 1996; Cox and Kobayashi, 2000; Govender et al., 2002;
Stansby and Feng, 2005; De Serio and Mossa, 2006; Shin and Cox, 2006; Kimmoun and Branger, 2007; Huang
et al., 2009; Sou et al., 2010; Ting and Nelson, 2011; Sumer et al., 2013]. Ting and Kirby’s studies [1994, 1995,
1996] have shown that the production and transport of turbulent kinetic energy (TKE) are different for dif-
ferent breaker types. Plunging breakers lead to an injection of TKE into the water column, which is rapidly
advected downward by the plunging jet and large vortices. Turbulence under plunging waves is further
characterized by strong dissipation, which leads to a large temporal variation in TKE throughout the wave
cycle. Since most transport of TKE takes place rapidly after injection during the wave crest, net transport of
TKE is in the onshore direction [Ting and Kirby, 1994; De Serio and Mossa, 2006]. Under spilling breakers, tur-
bulence is more gradually entrained into the water column by diffusion, and dissipation rates are lower,
leading to a fairly constant time-variation in TKE throughout the wave cycle and net transport of TKE in the
offshore direction as a result of the undertow. Assuming that suspended sediment transport is linked to the
turbulence transport, these two mechanisms may partly explain onshore sandbar migration during calm
swell wave conditions (plunging waves) and offshore migration under stormy conditions (spilling waves)
[Ting and Kirby, 1994].
Although breaking wave characteristics over a barred profile may differ significantly from those on a plane
sloping beach [Smith and Kraus, 1991], relatively few laboratory studies examined the velocity and turbu-
lence characteristics of waves breaking over a bar. Existing studies which included turbulence measure-
ments under breaking waves over a barred profile have been conducted in small-scale wave flumes with
fixed beds [Boers, 2005; Govender et al., 2011] and in large-scale wave flumes with fixed [Scott et al., 2005] or
mobile beds [Yoon and Cox, 2010; Brinkkemper et al., 2016; van der Zanden et al., 2016]. Most of these studies
showed a strong cross-shore variation across the bar with TKE being highest on, or slightly shoreward of,
the bar crest where the waves are breaking [e.g., Boers, 2005; Scott et al., 2005; Yoon and Cox, 2010; van der
Zanden et al., 2016] and that at these locations breaking-induced TKE may reach the bed [Scott et al., 2005;
van der Zanden et al., 2016]. In the bar trough, the TKE profiles showed a local minimum compared to adja-
cent locations since the TKE is mixed over a greater water depth [Yoon and Cox, 2010]. Boers [2005] correlat-
ed the orbital velocity to the TKE and identified in the vicinity of the breaker bar a phase lag between the
production of turbulence near the water surface (during wave crest phase) and the arrival of turbulence at
the bed (during wave trough phase). At the other locations in the surf zone the correlation appeared to be
minimal. A strong phase coupling between the turbulence and orbital motions under plunging waves was
also found in a recent large-scale experiment by Brinkkemper et al. [2016]. Their ensemble-averaged results,
for three elevations at one surf zone location, reveal highest intrawave TKE at the wave front. They also
showed that under their full-scale rippled bed conditions where the boundary layer is turbulent, the bed-
generated TKE can have similar magnitude as the TKE closer to the water surface.
While useful insights have been obtained from the breaking wave studies on plane sloping beach profiles it
is evident that the flow and turbulence fields under breaking waves on barred profiles are significantly dif-
ferent, yet much less studied. Moreover, most of the existing studies have focussed primarily on the time-
averaged flow and turbulence, and not on the detailed intrawave flow and (horizontal and vertical transport
of) turbulence around the bar, which ultimately are important to understand the sediment transport
dynamics. The aim of the present experiment was therefore to obtain such detailed measurements of the
flow and turbulence under a large-scale plunging breaking wave around a fixed breaker bar. The experi-
ment was conducted in the large-scale CIEM wave flume as part of a larger experimental campaign to study
hydrodynamics and sediment transport processes under breaking waves. Measurements of near-bed hydro-
dynamics and turbulence under a breaking wave over a mobile bed, obtained as part of this project, were
reported in van der Zanden et al. [2016]. The fixed bed experiment described in the present paper involves
the same wave condition as in
van der Zanden et al. [2016]. The experiment distinguishes itself from previ-
ous barred profile experiments by the high spatial resolution of the measurements, the use of high-
Journal of Geophysical Research: Oceans 10.1002/2016JC012072
van der A ET AL. BREAKING WAVE HYDRODYNAMICS 3288
resolution optical instrumentation (LDA) and a regular wave condition which enables us to get insight into
the intrawave velocities and turbulence, while the large-scale of the experiment further ensures that turbu-
lence generated in the boundary layer is representative of field-scale conditions.
Section 2 of the paper describes the experiment and the data processing methods. The results are pre-
sented in four sections as follows: water surface elevation results are presented in section 3; intrawave and
time-averaged horizontal and vertical velocities are presented in section 4; section 5 presents time-
averaged TKE, turbulence intensities and Reynolds shear stress along the profile; section 6 presents an anal-
ysis of the TKE transport, production and dissipation across the barred profile, from the shoaling zone
through to the inner surf zone. The results are discussed in section 7 and the main conclusions are summa-
rized in section 8.
2. Experiments
2.1. Experimental Facility and Bed Profile
The experiment was conducted in the 100 m long, 3 m wide, and 4.5 m deep wave flume at the Polytechnic
University of Catalunya in Barcelona (Figure 1a). The wave generation system consists of a wedge-type
wave paddle and the steering signals were based on first-order wave generation. The coordinate system
has its x origin at the toe of the wave paddle in its rest position and is positive in the direction of the waves;
the vertical z coordinate has its origin at the still water level and is positive upward; the y coordinate has its
origin on the right side wall of the flume when facing the beach and is positive toward the center of the
flume. Throughout this paper g is the water surface elevation,
g the mean water level (mwl), h the water
depth, H the wave height, and subscript p indicating wave height (near the paddle) in the constant depth
section of the flume; u, v, and w are velocity components in the x, y, and z directions, respectively.
The beach profile for the fixed bed was created in a preceding experiment [van der Zanden et al., 2016] by
running the same regular wave condition as used in the present experiment for 3 h over a mobile sand bed
profile (sand grain diameter d
50
5 0.25 mm), which initially consisted of a 1:10 offshore slope raised to
1.35 m above the flume floor, followed by a 18 m long horizontal bed, and terminated by a nonmobile
straight sloping beach. The rather long horizontal section was chosen in order to ensure that bed slope
effects in the inner surf zone or swash zone processes did not affect the hydrodynamics around the bar.
After 3 h of waves a breaker bar was created that was sufficiently high to ensure a strongly plunging wave
Figure 1. (a) Fixed bed profile and the locations of the resistive wave gauges and pressure transducers; (b) close-up of the velocity mea-
surement area around the breaker bar showing the positions of the ADV and LDA velocity measurements.
Journal of Geophysical Research: Oceans 10.1002/2016JC012072
van der A ET AL. BREAKING WAVE HYDRODYNAMICS 3289
with a highly repeatable breaker location. We note that after 3 h the bar had not yet reached a morphody-
namic equilibrium, as can be seen in Figure 3 of Ribberink et al. [2014]. To construct the fixed bed, the top
10 cm layer of sand was removed from the profile and a 20 cm layer of concrete was added on top, which
was allowed to cure for approximately 40 days prior to the start of the experiment. The resulting fixed bed
profile consisted of a 1:12 offshore slope, a 0.6 m high breaker bar (measured from crest to trough), with a
lee-side slope of approximately 1:4, followed by a 10 m long 1:125 slope and terminated by a fixed 1:7 slop-
ing profile (see Figure 1). The profile corresponds approximately to the bed profile at t 5 60 min in the
accompanying mobile-bed experiment [van der Zanden et al., 2016]. The roughness of the concrete surface
was reasonably uniform across the profile and estimated to be of the order of 1–2 mm. On the lee-side of
the bar the roughness was approximately twice as large, due to cement leaking away on the steep slope
during the curing process, which exposed some of the coarser aggregates at the surface.
2.2. Test Condition
The water depth in the horizontal part of the flume was 2.65 m and the wave condition consisted of a regu-
lar wave with wave period T 5 4 s and a target wave height of H
p
50:85 m at the paddle. The surf similarity
parameter is defined as:
n
0
5
tan b
ffiffiffiffiffiffiffiffiffiffiffiffi
H
0
=L
0
p
(1)
where tan b is the 1:12 beach slope, H
0
is the deep water wave height which was obtained from a linear
wave shoaling calculation using the wave height in the constant depth section of the flume and the deep
water wave length L
0
5gT
2
=2p. n
0
50.44, which is consistent with the plunging breaker realized in the
flume and in agreement with Smith and Kraus’s [1991] classification for barred profiles. More details of the
wave breaking characteristics will be presented in section 3. In each ‘‘run’’ waves were generated for a dura-
tion of 38 min.
2.3. Measurements
Water surface elevations were measured with sidewall-mounted resistive wave gauges at 19 locations along
the flume, from x 5 12 m in the constant depth section of the flume to x 5 49 m in the shoaling zone
(Figure 1a). Resistive wave gauges were not deployed in the surf zone since they suffered from spurious
measurements due to the strong splash-up of water. For the remainder of the profile, pressure transducers
(STS-ATM/N) were therefore fitted along the flume sidewall at approximately 0.5 m x spacing. Water surface
elevations were retrieved from the pressure measurements after correcting for pressure attenuation due to
depth using linear wave theory. Comparison of water surface elevation measured by collocated pressure
sensors and resistive wave gauges at two locations in the prebreaking area showed good agreement, with
maximum difference of approximately 10%. The
resistive wave gauges and pressure transducers
were sampled at 40 Hz.
Velocities were measured at 12 cross-shore loca-
tions along the bar region (Figure 1b) using
a Laser Doppler Anemometer (LDA) and two
Acoustic Doppler Velocimeters (ADV) deployed
from a measurement frame attached to a car-
riage on top of the flume (Figure 2). This ‘‘mobile
frame’’ allowed the instruments to be positioned
at any cross-shore location with 1 cm accuracy
and in the vertical with 1 mm accuracy [for more
details on the frame, see Ribberink et al., 2014].
The two-component backscatter LDA system
consisted of a 14 mm diameter submersible
transducer probe with 50 mm focal length pow-
ered by a 300 mW Ar-Ion air-cooled laser. The
LDA measured the u and w velocity components
in an ellipsoidal shaped measurement volume of
Figure 2. Mobile measurement frame indicating the instrumentation
positions Note that the instrument on the bottom right (3C-Acoustic
Doppler Velocity Profiler) was not used for the pres ent study.
Journal of Geophysical Research: Oceans 10.1002/2016JC012072
van der A ET AL. BREAKING WAVE HYDRODYNAMICS 3290
115 lm maximum diameter and approximately 2 mm length in the y direction. For given seeding particle
density, the sampling frequency of the LDA depends on velocity magnitude and, therefore, varies through-
out the wave cycle. Data rates for the present experiment typically varied between 100 and 600 Hz.
Three-component velocity measurements were obtained from the ADVs (Nortek Vectrino), one of which
was positioned on the same side of the frame as the LDA, while the other (ADV2) was positioned on the
other side of the frame (Figure 2). The size of the cylindrical shaped measurement volume of both ADVs
was 6 mm in diameter and 2.8 mm in length in the y direction. The vertical spacing between the LDA and
ADV1 was 0.33 m and between the LDA and ADV2 was 0.83 m. The ADV sampling frequency was 100 Hz.
The mobile frame also contained a pressure transducer (PT
frame
) to measure water surface elevation at the
frame measurement location (Figure 2a).
The mobile frame could be vertically repositioned during a wave run, allowing typically three vertical mea-
surement positions to be covered during one wave run. At each cross-shore measurement position, LDA
velocities were measured at 1, 5, and 10 cm above the bed, and at 10 cm vertical increments higher
up, until the limit of the frame’s vertical movement was reached, which corresponds to the LDA reaching
z 520:47 m. The lowest measurements for ADV1 and ADV2 were at 34 cm and 84 cm above the bed,
respectively, and the remaining ADV measurement elevations followed the same incremental changes as
the LDA, reaching maximum elevations of z520:13 m and z 5 0.37 m for ADV1 and ADV 2, respectively.
2.4. Data Processing
For each 38 min run (5570 waves), the first 400 s (5100 waves) of data were discarded because the hydro-
dynamics were still developing in the flume, which could be visually observed by a gradual change in the
wave breaking location. After 400 s the breaking location and breaking wave characteristics were stable,
indicating that the hydrodynamics in the breaking zone had reached a quasi-equilibrium state. The remain-
der of the time series was used to obtain ensemble-averaged quantities. All water surface and velocity data
were high-pass filtered with a cutoff frequency of 0.125 Hz (50:5=T) in order to remove the low frequency
(f 5 0.022 Hz) standing wave in the flume which had an amplitude of a few cm.
Data from the resistive wave gauges and the sidewall-mounted pressure transducers were averaged over
multiple runs since these instruments had fixed x locations. During a full 38 min run, the mobile frame mea-
surement frame covered three vertical elevations for a duration of 10 min each, which is equivalent to 150
waves for each ( x, z)-velocity measurement. A total of 150 waves for ensemble-averaging were similar to
Scott et al. [2005], and more than Ting and Kirby [1994] and Shin and Cox [2006], who used 100 waves.
Spikes in the ADV velocity data occurred as a result of air bubbles entrained by the wave breaking process.
This particularly happened at instances of intense plunging above the downward slope of the bar and in
the upper part of the water column throughout the inner surf zone. A combination of approaches was used
to despike the ADV velocity data. First the 3-D phase-space method of Mori et al. [2007] was applied to
remove spikes in the time series. Then, any data having correlation values below 80% and Signal-to-Noise-
Ratio (SNR) below 15 dB were identified as poor quality data in the time series. Finally, at the ensemble-
averaging stage, any data at a given wave phase that deviated by more than four standard deviations from
the median value at that phase was also considered an outlier. Poor quality of spurious velocity data identi-
fied during the last two steps was removed from the analysis of the data set. The proportion of data
removed depends strongly on the cross-shore location of the measurement and the phase of the wave, and
their occurrence in the time series could therefore vary between a few percent in the prebreaking area to
100% during certain phases at locations where the plunging jet penetrates the water column and air bub-
bles lead to significant attenuation of the acoustic signal. Phase-averaged velocities based on <15 wave
cycles, and turbulence results based on <40 wave cycles [Shin and Cox, 2006], were therefore excluded
from the results, which explains why there are ‘‘gaps’’ in the results presented later and why at most loca-
tions results are only shown below the wave trough level.
The LDA data suffered from fewer poor quality measurements because the data are SNR-validated instanta-
neously during acquisition, and, when a bubble traverses through the measurement volume or laser beam
paths the LDA records nothing rather than recording an erroneous measurement. Moreover, the LDA mea-
surement volume and the laser beams are significantly smaller than the ADV measurement volume and the
acoustic beams, which means there is less chance of a bubble obstructing the LDA measurement. The LDA
Journal of Geophysical Research: Oceans 10.1002/2016JC012072
van der A ET AL. BREAKING WAVE HYDRODYNAMICS 3291