JournalofofCoastal
CoastalResearch
Research
Journal
64
SISI64
pg
- pg- 2057
2053
ICS2011
ICS2011(Proceedings)
(Proceedings)
Poland
Poland
ISSN 0749-0208
Flume experiments on wave non-linear interactions effects on beach
morphodynamics
P. Prel†, H. Michallet† and E. Barthélemy†
† Laboratoire des Ecoulements Géophysiques et Industriels
(CNRS – UJF – INPG)
BP 53, 38041 Grenoble cedex 9, France
[email protected]
ABSTRACT
Prel P., Michallet M., Barthélemy E. 2011. Flume experiments on wave non-linear interactions effects on beach
morphodynamics. Journal of Coastal Research, SI 64 (Proceedings of the 11th International Coastal Symposium),
– . Szczecin, Poland, ISSN 0749-0208
Waves in the coastal zone are organized in groups. The breaking of those groups generates long waves. The
effects of these long waves on the beach morphology are quite misunderstood. Experiments in similitude with
nature were conducted in the LEGI wave flume in order to better understand non-linear interactions structures and
to assess their influence on morphodynamics. Bichromatic waves were generated in order to develop different
structures of standing waves. All conditions were tested on similar profiles characterized by a surf zone confined
on the upper beach. On the lower beach including the shoaling zone, the morphological evolutions are found to be
only induced by wave non-linearities and not influenced by breaking related effects such as undertow or
turbulence. Morphological evolutions are very different from a wave condition to the others: bar formation, bar
washing, bar displacement. Modulations of skewness and asymmetry were observed, related to both recurrence
phenomena and long wave modulation. They explain the morphological evolution. Although a role of infragravity
waves has been observed, bar formation is not consistently located under nodes or anti-nodes of the standing
waves.
ADDITIONAL INDEX WORDS: long wave, skewness, asymmetry, bar formation
INTRODUCTION
Waves in the coastal zone are organized in groups. The
propagation and breaking of these wave groups generate long
waves known as surf beat. Our understanding of the effects of the
surf beat on the beach morphodynamics is still fragmented. In
particular, long waves are suspected to be involved in sand bar
formation in the shoaling or surf zones. Indeed, there are two main
hypothesis to explain bar formation. According to Roelvink and
Stive (1989), the bar formation could be at the converging point
(in the breaking zone) of opposing undertow and skewed waves
effects on sediment transport. On the other hand, Holman and
Bowen (1982) suggested that bars could be the result of
converging sediment fluxes at standing wave nodes if bed load
dominates or antinodes if suspension dominates. Roelvink (1993)
studied numerically the influence of surf beat on surf zone
morphology and bar formation. He concluded that the latter is
strongly influenced by narrow banded surf beats. However Dally
(1987) experimentally found little evidence to support the role of
long waves in bar formation induced by bichromatic wave groups.
Baldock et al. (2010) recently studied the influence of free and
bound long waves and wave groups on sediment transport in the
surf and swash zones. In contrast, the present study focuses on the
morphodynamics induced by standing waves offshore the
breaking point.
The experimental study of Grasso et al. (2011) as well as
numerical study of Ruessink et al. (2009) confirm the strong
influence of skewness and asymmetry (acceleration skewness) on
sediment transport intensity (Bailard, 1981) and direction. Grasso
et al. (2011) found little transport for very low skewness. For
higher values of skewness crest velocity increases and the
velocity decreases in the through, resulting in onshore sediment
transport. Beyond a threshold, the wave crest is so peaky that part
of the sediment stirred by crest velocities cannot settle; which is
then transported offshore by the through (phase-lag effects).
Asymmetry effects can modify these trends. Positive asymmetry
associated to pitched forward waves generates onshore transport
whereas negative asymmetry generates offshore transport. The
skewness and asymmetry influence on sediment transport is
difficult to study because it is hard to isolate those phenomena
from other breaking phenomena. Our study enables this since
appears recurrence that generates variations of skewness and
asymmetry away from the breaking zone.
EXPERIMENTAL SET-UP
Experiments were conducted in the LEGI wave flume (Fig. 1),
with internal dimensions of 36 m length and 0.5 m width, for
studying the long wave pattern produced by the short waves
breaking and to evaluate their influence on the morphodynamics.
Lightweight sediment (density 1.19 and median diameter 0.6 mm)
is used in order to fulfill scaling laws and obtain experimental
beach profiles in similitude with the ones observed in nature
(Grasso et al., 2009). Length and time scales are 1/10 and 1/3,
respectively, and the sediment transport encompass bed load,
suspension and sheet flow regimes of coarse sands. A secondorder compensating generation (Sand, 1982) was imposed to the
piston wave-maker so that the bound long waves associated to the
wave groups are correctly reproduced. Free surface elevations are
measured with capacitive gages. The fluid velocities cross shore
distribution on the beach profile are measured with a Nortek
Vectrino. Fluid velocities are measured at 3 cm above the bottom.
Journal of Coastal Research, Special Issue 64, 2011
2053
Flume experiments on wave non-linear interactions effects on beach morphodynamics
Table 1: Characteristics of simulated bichromatics
f1(Hz)
f2(Hz)
∆f
Type
L1 (m) L2 (m)
Exp. 0
0.486
0.514
0.028
Detuned
6.1
5.0
Exp. 1
0.476
0.524
0.048
Uninodal
6.6
4.7
Exp. 2
0.460
0.539
0.089
Binodal
7.4
4.3
Exp. 3
0.445
0.555
0.110
Trinodal
8.3
3.9
In a first step, irregular waves conforming to a Jonswap
spectrum (significant wave height Hs=13.5 cm and peak period
Tp=2 s) are generated for more than 60 hours leading to a steep
beach profile at equilibrium with a mean slope of about 1/25. In
these conditions the breaking zone is close to the coastline (about
18 m) which enables the dissociation of morphological evolutions
related to breaking process from other bar formation mechanisms.
Besides, four bichromatic wave conditions with the same Hs are
generated in order to obtain different standing waves patterns. The
frequencies (f1 and f2) of the two sinusoidal components were
chosen so that Tp=2/(f2+f1) (see Table 1). For three of the
bichromatic conditions, the difference (f2-f1) was tuned with one of
the first three seiching modes of the flume. The fourth was a
detuned condition for which the value of (f2-f1) was chosen to
avoid a resonant mechanism. The four bichromatic wave
conditions thus lead to uninodal (Exp.1), binodal (Exp.2) and
trinodal (Exp.3) patterns and no standing wave (Exp.0).
All bichromatic conditions are run twice on similar initial
profiles (close to equilibrium profile of Jonswap spectrum),
characterized by a surf zone confined on the upper beach. On the
lower beach including the shoaling zone, the morphological
evolutions are found to be only induced by wave non-linearities
and not influenced by breaking related effects such as undertow or
turbulence. In all experiments, the Shields number on the lower
part of the beach is less than 0.7 so that a ripple regime with
mainly bed load transport was observed.
RESULTS: WAVE CHARACTERISTICS
Figure 2 shows spectrum measured at 2 m from wave maker for
the four simulated conditions. Theoretical resonance frequencies
were calculated from a Saint Venant model for each beach profile.
Peaks of frequency (f2-f1) and their harmonics are predominant in
low frequency domain. Resonance frequencies are visible but
weaker. When (f2-f1) peak matches with resonance frequency, its
power spectral density is about 100 times more important.
Experiments were all carried out twice and same morpholocical
evolutions were observed. Total energetic wave heights (Hrms) are
very close from a wave condition to the other. It enables a
comparison between the different experiments. Morphological
evolutions are very different from a wave condition to the other.
As shown in figure 3, experiment 0 leads to the formation of a bar
at 8 m. It is located at 10 m in experiment 3 (Fig. 4). Sediment
spreads offshore then a bar is formed at 8 m in experiment 2.
Finally, experiment 1 leads to an equilibrium profile without bar
formation.
Cross-shore distribution of energetic wave heights related to
low-frequency peaks conforms expectations. Nodal structures are
very well represented and energy held in (f2-f1) peak is obviously
important. Nodal structure can also be seen in velocity measures.
For x<15m, free surface elevation nodes clearly match with
velocity antinodes and vice versa. Beyond, water depth is too
small to have accurate measures of velocity.
Despite strong standing wave patterns, sediment accumulation
was not preferentially observed at either a node or an anti-node
position. Bars are formed under nodal position (Exp.3), between
nodal and anti-nodal (Exp.2), without a nodal structure (Exp.0) ou
are washed (Exp.1).
The analysis of the free surface elevations reveals a recurrence
mechanism resulting from the interaction between the forced and
free harmonics (see Mei, 1992; the corresponding theoretical
wavelengths are indicated in Table 1). The phenomenon is
obvious when (f2-f1) is small enough (Exp.0 and Exp.1). The
skewness Sk1 clearly responds to this recurrence. When (f2-f1) is
larger, there is a superimposition of different recurrence
phenomena (at frequency f2, f1, (f2+f1)/2) that blur the picture.
Harmonic recurrence produces cross-shore variations of velocity
skewness and asymmetry which are thoroughly studied hereafter.
Skewness and asymmetry are (see, e.g., Michallet et al., 2011):
(1)
(u − u )3
Sk =
As = −
3/ 2
u2
Η3 (u − u
u
)
(2)
2 3/ 2
Velocity is splitted into high and low frequency components
inducing the following break-down for the skewness:
(3)
u − u = u HF + u LF
u HF >> u LF
(u − u )
3
3
2
2
= u HF + 3u HF u LF + 3u HF u LF + u LF
3
(4)
Thereby u is splitted into four terms (Marino-Tapia et al.,
2007). The first two terms dominate. The associated skewness
read:
3
Figure 1. Schematic diagram of the LEGI flume
Journal of Coastal Research, Special Issue 64, 2011
2054
Sk1 =
u HF
u
3
2
Sk 2 =
(5)
2 3/ 2
3 u HF u LF
u2
3/ 2
(6)
Prel et al.
The Sk2 part of the skewness is not strictly speaking the lowfrequency skewnes, it has more to do with the correlation of the
the high-frequency energy with the low frequency motion.
The high frequency component of the velocity is similar for
each wave condition. Low frequency component is different
(standing wave patterns). Mean velocity (undertow) is close to
null in the shoaling zone for x<15 m.
Spatial evolution of skewness and asymmetry are very uneven
from an experiment to the other. Skewness can be low at each
position on the beach (Exp. 0), or very high. For instance, Sk is
close to 1 at x~7 m and x~17 m in Exp.2. The skewness pattern
over-all matches the low-frequency velocity component pattern
has can be seen for Exp.1, 2 and 3. Values of skewness are
observed in some instances to be negative, which is unusual. This
is clearly linked due to Sk2. Strong negative values of Sk2 indicate
anti-correlation of high frequency wave energy with low
frequency motion. On the contrary, Sk1 patterns, which represent
short wave skewness, are similar in every experiment for x<15 m
and its slight modulations are likely to result from recurrence
phenomena. Indeed, pseudo-periods of modulations are close to
theoretical calculations of recurrence phenomena induced by
(f2+f1)/2 that is to say about 5.5 m.
Temporal evolutions of skewness, indicated with the size of the
symbols, are very small, apart in experiment 2. In the last case, the
bar formation at x about 6 m disrupt skewness (from -0.3 to 0.8)
and asymmetry values.
MORPHOLOGICAL ANALYSIS
It seems that the small modulations of skewness and asymmetry
of Exp.0 induce sediment transport gradients for x<15 m. Indeed,
positive values of asymmetry (at x~5 m and x~14 m) could be a
major factor for onshore transport whereas slightly negative values
contribute to offshore transport at x~10 m or at least diminution of
transport generates an accumulation of sediment. However, it is
surprising that low modulations lead to a significant transport
(qs~3.10-6 m2/s at x~10 m). Undertow is dominant on upper
shoreface (x>15 m). Modulation is weak for Sk2 hence the
skewness modulation is attributed to Sk1, with a wavelength of
roughly 5.5 m, that fits to recurrence wave length.
The net sediment transport rate is very small in Exp.1 despite
nonzero values of skewness and asymmetry. It can explained as a
trade off between positive asymmetry (onshore transport) and
negative skewness (offshore transport). For x~15 m, highly
positive values of asymmetry lead to onshore transport.
In Exp.2 the skewness and asymmetry evolve strongly in time.
This is basically related to Sk2 time evolutions. On the lower shore
face (x<14 m) Negative values of asymmetry, a slight undertow
due to breaking on the bar as well as strong positive values of
skewness (triggering phase-lag effects) lead to a strong offshore
transport. On the upper beach the strong positive asymmetry
enables to offset the undertow effect as well as the strong
skewness.
In Exp.3 the skewness and the asymmetry modulate but the
asymmetry is overall negative pointing at a negative sediment flux
which is not compensated for by the skewness which remains
below the bounds that lead to phase lag effetcs. Two bars are
formed at x~2 m and x~10 m. In this conditions modulations of
skewness are again related to Sk2.
Sediment fluxes related to these evolutions are small compared
to morphological evolutions studied in Grasso et al. (2011). Exp.2
has the nearest results to Grasso’s observations, with strong
evolutions of the skewness and the asymmetry with a sediment
fluxes of about 5.10-6 m2/s.
CONCLUSIONS
Non-linear interactions of two high frequency components of
bichromatics wave produce long wave. For some couple of
frequency (f1, f2), long wave frequency match with resonance
frequency related to topography and produce standing wave.
The standing wave patterns contribute to modulation of skewness
and asymmetry which lead to morphological evolution. It seems to
correspond to the scheme proposed by Grasso et al. (2011) on
skewness and asymmetry effects. Although a role of infragravity
waves has been observed, bar formation is not consistently located
under nodes or anti-nodes of free surface standing waves. A bar
can form even without a standing wave pattern.
Figure 2. Spectrum measured at 2 m from wave maker for the four conditions simulated. Frequency of the first seiching modes of
the flume (diamonds) and frequency of the harmonics n(f2-f1) with n=1, 2, 3 (stars).
Journal of Coastal Research, Special Issue 64, 2011
2055
Flume experiments on wave non-linear interactions effects on beach morphodynamics
LITERATURE CITED
Bailard J.A., 1981, An Energetics Total Load Sediment
Transport Model For a Plane Sloping Beach, Journal of
Geophysical Research, 86, C11, 10,938-10,954.
Baldock T.E., Manoonvoravong P., Kim Son Pham, 2010.
Sediment transport and beach morphodynamics induced by free
long waves, bound long waves and wave groups, Journal of
Coastal Engineering. doi:10.1016/j.coasteleng.2010.05.006
Dally, W. R., 1987. Longshore bar formation – surf beat or
undertow? Proc. Coastal Sediments, 1987, ASCE, 71-85.
Grasso F., Michallet H. and Barthélemy E., 2011. Sediment
transport associated with morphological beach changes forced by
irregular asymmetric-skewed waves. Journal of Geophysical
Research, doi:10.1029/2010JC006550
Grasso F., Michallet H. and Barthélemy E., 2009. Physical
modeling of intermediate cross-shore beach morphology :
transients and equilibrium states. Journal of Geophysical
Research. 114, C09001.
Holman, R.A. and Bowen, A.J., 1982. Bars, bumps and holes :
Models for generation of complex beach topography. Journal of
Geohysical Research, 87, 457-468.
Marino-Tapia, I.J., Russel, P.E., O'Hare, T.J., Davidson, M.A.,
and Huntley, D.A., 2007, Cross-shore sediment transport on
natural beaches and its relation to sandbar migration patterns: 1.
Field observations and derivation of a transport parameterization,
Journal of Geohysical Research, 112, C03001.
Michallet H., Cienfuegos, R, Barthélemy, E, Grasso, F., 2011.
Kinematics of waves propagating and breaking on a barred beach
Eur. J. Mech.-B/Fluids, doi:10.1016/j.euromechflu.2010.12.004.
Mei, C.C. (1992), The Applied Dynamics of Ocean Surface
Waves, Adv. Ser. Ocean Eng., vol. 1, 2nd ed., World Sci.,
Hackensack, N. J.
Roelvink, J.A., 1993. Surf beat and its effect on cross-shore
profiles, The Netherlands: Technische Universiteit Delft, PhD.
thesis.
Roelvink, J.A. and Stive, M.J.F., 1989. Bar-generating crossshore flow mechanisms on a beach. Journal of Geohysical
Research, 94(C4), 4785–4800, doi:10.1029/JC094iC04p04785.
Ruessink B.G. , van der Berg T.J.J. and van Rijn L.C., 2009.
Modeling sediment transport beneath skewed asymmetric waves
above a plane bed. Journal of Geophysical Research. 114,
C11021.
Sand S.E., 1982. Long wave problems in laboratory models.
Journal of the Waterway, Ports, Coastal and Ocean Division, 108,
492-503.
ACKNOWLEDGEMENTS
Figure 3. Exp.0. From top to bottom : Root mean square
wave height Hrms, from wave-by-wave analysis (o) and (x) for
the low frequency component; orbital velocity of high
frequency (o) and low frequency (x) components; mean
velocity; wave skewness Sk (o) and asymmetry As (∆); Sk1 (o)
and Sk2 (*); mean sediment transport rate qs; initial (--) and
final (–) beach profiles. The size of the symbols indicates the
moment of the measurements from the beginning (small) to the
end (big) of the morphological evolution.
This research was sponsored by the MODLIT project
(DGA/SHOM – INSU/RELIEFS) and ANR BARBEC. We are
grateful for the technical support of Jean-Marc Barnoud and for
stimulating discussions with Florent Grasso and Céline Berni.
Journal of Coastal Research, Special Issue 64, 2011
2056
Prel et al.
Figure 4. Same legend as figure 3, from left to right : Exp. 1, Exp. 2, Exp. 3.
Journal of Coastal Research, Special Issue 64, 2011
2057