Morphology and dynamics of subaqueous dunes generated under unidirectional flow

Abstract

The flow velocity over mobile sandy dunes subjected to unidirectional current was investigated using a UB-Lab 2C, an acoustic velocity profiler newly developed by UBERTONE. A space-localized wavelet approach was used in order to detect the temporal evolution of the main dune’s wavelength. The acoustic tool has provided promising results concerning the flow and sediment dynamics over migrating dunes.

Full text

Marine and River Dune Dynamics – MARID VII – 1-3 April 2023 - Rennes, France
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1 INTRODUCTION
Dunes in natural marine environments are
subject to various, complex and unsteady
hydrodynamic forcings. Understanding and
forecasting their morphology and dynamics
is an important task, especially when
interacting with marine structures, as the
bedform-related roughness strongly
influences sediment transport. In shallow
waters and intertidal environments in
particular, subaqueous dunes are strongly
influenced by waves which combine with
unidirectional or reversing currents. Their
morphology can also be strongly modified by
extreme events. Physical experiments in
flumes constitute a common approach to the
study of natural systems that helps to test
independently the influence of each forcing
occurring in nature. To date, most of the
physical experiments conducted on marine
dunes in flumes have been performed under
unidirectional steady current (Blom et al.,
2003; Boguchwal and Southard, 1990;
Bridge and Best, 1988; Kleinhans, 2004;
Naqshband et al., 2014), or under long-period
oscillating flows in tunnel flumes (Perillo et
al., 2014). Thus, there is still a need to
explore how dunes grow in the presence of
currents interacting with short-period waves,
longer storm waves or extreme events, and to
understand how waves modify the dune
morphology, in comparison with current-
only dynamic equilibrium morphology.
In this paper, we present preliminary
experiments of a study which aims at
understanding, using physical experiments,
the response of dunes to wave-current
interactions. We report the development,
equilibrium morphology and flow structure
of dunes under unidirectional current, a
simple flow condition which will serve as a
comparison for future experiments using
combined flows. Dune growth and
equilibrium morphology was surveyed
thanks to a laser distance meter, and a space-
localized wavelet approach was used in order
to detect the temporal evolution of the main
dune’s wavelength. Quantitative information
on flow structure and sediment transport was
obtained by deploying the UB-Lab 2C, a new
acoustic Doppler profiler manufactured by
UBERTONE, which provides high spatial
and temporal measurement of both two-
component flow velocity and sediment
concentration profiles over the entire water
column.
The information of sediment
concentration can be derived from the UB-
Lab 2C backscatter intensities following the
methodology of Hurther et al. (2011). This
Morphology and dynamics of subaqueous dunes generated under
unidirectional flow
I. Abroug Normandie université, UNICAEN, UNIROUEN, CNRS, UMR 6143 M2C, 14000 Caen, France
– iskander.abroug@unicaen.fr
P. Weill Normandie université, UNICAEN, UNIROUEN, CNRS, UMR 6143 M2C, 14000 Caen, France –
pierre.weill@unicaen.fr
N. Abcha Normandie université, UNICAEN, UNIROUEN, CNRS, UMR 6143 M2C, 14000 Caen, France –
nizar.abcha@unicaen.fr
ABSTRACT: The flow velocity over mobile sandy dunes subjected to unidirectional current was
investigated using a UB-Lab 2C, an acoustic velocity profiler newly developed by UBERTONE. A
space-localized wavelet approach was used in order to detect the temporal evolution of the main
dune’s wavelength. The acoustic tool has provided promising results concerning the flow and
sediment dynamics over migrating dunes.

Marine and River Dune Dynamics – MARID VII – 1-3 April 2023 - Rennes, France
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offers the ability to explore sediment flux
profiles in the suspension layer. The
inversion from intensity to concentration is
done by iterating downdwards from the
emitter while accounting for the signal
attenuation occurring along the water depth,
as described in detail by
Batteridge et al. (2008) and
Thorne and Hurther (2014). The
interpretation of the acoustic backscatter
intensity requires calibration of the system. In
this study, dimensionless concentration
results will be given as to date, the calibration
system is still under development.
2 MATERIAL AND METHODS
The present data were acquired within the
MOdelling of marine DUnes: Local and
Large-scale EvolutionS in an OWF context
(MODULLES) project. The tests have been
carried out in the wave and current
circulating flume of the M2C laboratory
located in Caen (France). The flume is 16 m
long, 0.5 m wide and 0.5 m deep, and is
equipped with a piston type wave maker and
a centrifugal pump for water recirculation.
In order to ensure the uniformity of the
flow, a 20 cm-high honeycomb was installed
at the entrance of the flume, followed by a 1
m-long pebble bed to ensure the fast
development of a turbulent boundary layer. A
sediment trap was also installed at the end of
the flume to collect the bedload sediment.
The longshore coordinate x was defined as 0
at the beginning of the sandy bed (Figure 1),
increasing toward the other end of flume and
the still water depth was 0.3 m. For present
tests, a coarse sand of median diameter
D50 = 0.6 mm and relative density
s = ρ/ρs = 2.65 is selected based on the
bedform phase diagram (Southard and
Boguchwal, 1990).
Figure 1. A schematic showing the experimental setup
in the test section of the water flume.
The flow velocity was measured with the
totally submerged UB-Lab 2C. The UB-Lab
2C allows to acquire co-located two (2C)
instantaneous velocity profiles with three
transducers (2 emitters and 1 receiver). The
two instantaneous velocity components are
denoted (u,v) along the directions (x,z)
respectively. Figure 2 shows a comparison
between a velocity profile u(z) given by the
UB-Lab 2C and a velocity profile given by
the two well established instruments, the PIV
and the ADV.
Figure 2. Comparison between velocity profiles u(z)
given by the UB-Lab 2C and (a) PIV measurements
(b) ADV. The averaging time for the two acoustic
tools is 2 minutes and 30 s for the optical tool. The
sampling frequency is 20 Hz for UB-Lab 2C, 100 Hz
for the ADV and 200 Hz for the PIV.

Marine and River Dune Dynamics – MARID VII – 1-3 April 2023 - Rennes, France
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The experimental procedure was
conducted as follows. First, the sandy bed
installed over 9 m was flattened to reach a
thickness of 10 cm (around 0.5m3 of sand).
The uniform current U = 0.65 m/s was then
generated in the flume and UB-Lab 2C flow
and concentration measurements were
performed. Experiments were stopped every
15 minutes to collect the sand trapped
downstream and to reinject it upstream, as the
sediment was not recirculated automatically.
The overall duration of the experiment was
around 300 min.
The 9m-long sandy bed topography was
surveyed every 15 minutes along 5 parallel
longitudinal transects, using a laser distance-
meter mounted on a carriage. The
longitudinal profiles were then interpolated
to obtain maps of the bottom topography.
3 RESULTS AND DISCUSSION
3.1 Topography evolution of dunes
Starting from plane bed, ripples appeared
instantaneously as the flow was introduced in
the flume. Dunes subsequently developed
and finally a steady state condition was
obtained where the dunes migrated
through the flume with a relatively constant
speed. Figure 3 shows 20 selected maps of
the bed evolution in time along the effective
measuring section of the flume. Quasi
equilibrium state is here defined as the
moment when dunes morphologic
characteristics (mean wavelength and height)
does not change substantially.
Topographic instantaneous profiles are
overlaid chronologically at regular time
intervals (i.e., 15 min) in order to plot the
space-time diagram (Figure 4) which was
used to calculate the dune velocity
(U ~ 2 m/h) at equilibrium.
Figure 4. The space-time diagram which reflects the
topography along time.
Figure 3. Bed temporal evolution along the flume.

Marine and River Dune Dynamics – MARID VII – 1-3 April 2023 - Rennes, France
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3.2 Wavelet analysis
Wavelet analysis was used to study spatial
series bed elevation profiles acquired every
15 min. The objective is to be able to account
for the variability of the signal frequency at
the different positions along the study
section. The continuous wavelet transform
WT(a,τ) of the topography spatial signal,
xn(t), is defined as a convolution integral of
xn(t) with a mother wavelet, 
 that is
translated and scaled along the signal:
󰇛 󰇜  


 (1)
(1)
where the asterisk indicates the complex
conjugate, ψ(a,τ) represents the mother
wavelet function dilated by a factor τ and
scaled by a factor a, and dx the spacing. The
mother wavelet can be dilated by a factor τ
and scaled by a factor a. Scales can be written
as fractional powers of two:
       (2)
(2)
  
󰇛
󰇜 (3)
(3)
Where a0 = 0.005 is the smallest
resolvable wavelength, M the largest
wavelength, and δ the scale factor. The
selected scale factor was δ = 0.0005, giving a
total of 382 wavelengths. The space sampling
and the number of points were, respectively,
Δx = 0.005 m and N = 2000. The selection of
the mother wavelet was made based on
several tests performed in the data. Finally, a
complex Morlet mother wavelet was used, in
accordance with the suggestion by Cataño-
Lopera et al. (2009) and with the results
obtained by Gutierrez et al. (2013) in the
analysis of the capability of different mother
wavelets to retrieve ripple periodicities from
synthetic signals. The complex Morlet
wavelet can be interpreted as a sine wave
multiplied by a gaussian envelope.
The wavelet transform WT (a,τ) is here
displayed as a 2D colour plot (Figure 5)
showing wavelength versus space (distance
along the flume), with the colours
representing the magnitudes of |WT(a,τ)|².
Initially, between 30 and 75 min, the
evaluated wavelengths corresponded to
wavelengths ranging between 1 m and 1.4 m,
which is a currently accepted length criteria
to define dunes in the
literature (Ashley, 1990). Figure 5 shows that
the most energetic wavelengths vary
temporally. From 30 to 200 min, the extremes
correspond to wavelengths of around 1.2 m
and 1.6 m. With increasing time (t > 200
Figure 5. Wavelet magnitude for dunes resulting from steady current during the 285 min of experiments
and their corresponding mean wave power for each wavelength.

Marine and River Dune Dynamics – MARID VII – 1-3 April 2023 - Rennes, France
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min), a noticeable energetic band centred at
λ = 1.8 m appears. Figure 6 summarizes the
temporal evolution of the λ – distance along
the flume relation. It is found that at
t > 200 min, no noticeable changes are
observed in the dune’s main wavelength and
height (~ 9.5 cm).
Figure 6. Temporal evolution of dune’s wavelengths.
3.3 Flow and concentration analysis
The UB-Lab 2C probe was placed
downward-looking at x = 7 m and the dunes
migrated underneath it with a relatively
constant velocity. The acoustic tool provides
flow velocity and sediment concentration
profiles of 23 cm length and pulse repetition
frequency (PRF) of 900Hz at high spatial
(3 mm) and temporal resolution (20 Hz).
The sediment concentration estimation is
based on a statistical model of the recorded
squared voltage (Equation 4). It is derived
from semi-theoretical and experimental
determinations of the acoustical
backscattering and attenuation properties and
it is valid under incoherent scattering
conditions (Thorne and Hurther, 2014).
  󰇡
󰇢

󰇛󰇜 (4)
r is the range from the emitter which
varies between 0.05 m and 0.3 m, Ψ
represents the departure from the signal
spreading within the transducer nearfield and
R is the system constant. Ks represents the
sediment backscattering properties, αs is the
attenuation due to suspended sediment
scattering and αω is the sound attenuation due
to water absorption. A typical example of the
relative root-mean-square backscatter signal
Vrms is shown in Figure 7. The first 0.09 m
data are not shown because this part of
measurements is contaminated by the
crosstalk between the transmitter and the
receiver during the acquisition. Figure 7
shows a decreasing trend of the backscattered
signal with depth due to the r-1 term in
Equation 4.
Figure 7. Typical measurements of the relative
backscatter signal with range in the flume.
Bed elevation were extracted from the
UB-Lab 2C backscattered signal intensity.
One example of the bed detection is shown in
Figure 8. The sudden and large increase of
the backscattered signal intensity
corresponds to the bottom echo, and agrees
well with the location of zero-velocity on the
horizontal velocity profile.
Figure 8. Example of bed detection based on mean
backscattered signal intensity profile (bottom) and
mean streamwise velocity profile (top).
Figure 9a shows the contour map of the mean
streamwise flow velocity  evolution with
time. The position of the dune topography is

Marine and River Dune Dynamics – MARID VII – 1-3 April 2023 - Rennes, France
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detected thanks to the UB-Lab 2C
backscattered signal and is represented by a
solid black line. The flow is from right to left.
From Figure 9a, we can distinguish three
main flow features over the migrating dune.
The first feature concerns the presence of a
zone of deceleration in the lee side zone.
Negative streamwise velocities (counter-
currents) are localized in the through region,
and associated to the recirculating cell. The
second feature is the presence of an
acceleration zone in the stoss side region of
the dune with high streamwise velocities. The
third feature is the development of a
millimetric internal boundary layer on the
dune crest. These results are qualitatively
similar to those found in
Naqshband et al. (2014).
Figure 9b shows the contour maps of the
mean vertical  flow velocities along the
migrating dune. The main feature in this
figure is the presence of positive vertical
velocities almost along the entire migrating
dune.
Figure 9c represents the contour map of
the dimensionless sediment concentration
along the migrating dune. Two zones of high
sediment concentration are observed. These
are associated to (1) the lee side of the dune,
where significant sediment deposition occurs
by avalanching from the crest, and by settling
in the decelerating recirculation zone; (2) the
boundary layer reattachment point, where
significant erosion occurs during turbulent
bursts.
Figure 9. (a) Contour map of the mean streamwise
flow velocity . (b) Contour map of the mean vertical
flow velocity . (c) Contour map of the mean
dimensionless sediment concentration. The solid black
line shows the dune profile.
4 CONCLUSIONS AND PERSPECTIVES
This paper presents a study of the
morphology, dynamics, flow structure and
sediment concentration over a migrating
dune under unidirectional current, using
physical experiments. The wavelet approach
was used to quantify the mean dune
wavelength and its evolution with time. It
takes into account the variability of the
wavelengths along the flume extension, and
so, it permits the identification of the dune
wavelengths in different sections. This study
strengthens the utility of the UB-Lab 2C
acoustic tool in detecting flow and
concentration features over migrating dunes.
For the near future, we plan to perform the
calibration of the backscattered signal in
order to obtain quantitative results
concerning the concentration and the flux
above the migrating dune. Morever, in order
to expand results found in this study, new
tests involving the presence of regular and
irregular waves propagating on the

Marine and River Dune Dynamics – MARID VII – 1-3 April 2023 - Rennes, France
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background of a steady current will be
performed. To our knowledge, there has not
yet been flume experiments investigating
dune dynamics under extreme waves.
Therefore, there is a strong need to conduct
experiments on dune dynamics in the
presence of group focused waves in order to
derive general formulation and deepen our
knowledge of dune morphodynamics under
nonlinear forcings.
5 ACKNOWLEDGEMENT
This study is funded by the Normandy
region, and is part of the project named
“MOdelling of marine DUnes: Local and
Large-scale EvolutionS in an OWF context
(MODULLES), supported by France
Energies Marine (FEM).
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