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Bedload transport and bedforms migration under sand supply limitation

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Mélanie Vah at Université Le Havre Normandie
Mélanie Vah
Armelle Jarno-Druaux at Université Le Havre Normandie
Armelle Jarno-Druaux
Sophie Le Bot at Université de Rouen Normandie
Sophie Le Bot
Yann Ferret
Yann Ferret
Yann Ferret
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Abstract and Figures

Most studies on sediment transport and bedforms migration consider unlimited sediment supply conditions. However, areas where the sediment supply is limited are common in coastal and fluvial environments. The present paper, based on physical modelling in a flume and on a re-analysis of field data obtained in the Eastern English Channel by Ferret (Morphodynamique des dunes sous-marines en contexte de plate-forme mégatidale (manche orientale). approche multi-échelles spatio-temporelles, 2011), considers the effects of sediment supply limitation on bedload transport and bedforms migration velocity. The bedload transport is found to be proportional to the fraction of the bed covered by sediments for a bed exhibiting bedforms. The migration velocity of bedforms depends on the dominant mode of sediment transport. A new formulation showing a good agreement with experimental tests and observations in the field is proposed for the dimensionless migration velocity of these bedforms when sediment transport is dominated by bedload, under unlimited sediment supply conditions. For limited sediment supply conditions and sediment transport dominated by bedload, an adaptation of the formulation is suggested from flume data sets, based on the fraction of the bed covered by sediment.
Current flume with the different experimental zones. a Side view, b top view
Current flume with the different experimental zones. a Side view, b top view
… 
Dune field in the Eastern English Channel in limited (western zone) and unlimited (central and eastern zones) sediment supply conditions. Field data from Ferret [23]. General bathymetry from Shom (Service hydrographique et océanographique de la Marine—France)
Dune field in the Eastern English Channel in limited (western zone) and unlimited (central and eastern zones) sediment supply conditions. Field data from Ferret [23]. General bathymetry from Shom (Service hydrographique et océanographique de la Marine—France)
… 
Variation of the dimensionless bedform migration velocity cinf/u∗′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_{inf}/u'_*$$\end{document} with (θ′-θc)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\theta '-\theta _c)$$\end{document} for unlimited sediment supply conditions
Variation of the dimensionless bedform migration velocity cinf/u∗′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_{inf}/u'_*$$\end{document} with (θ′-θc)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\theta '-\theta _c)$$\end{document} for unlimited sediment supply conditions
… 
Rouse number as a function of (θ′-θc)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\theta '-\theta _c)$$\end{document}. Symbols are defined in Fig. 11
Rouse number as a function of (θ′-θc)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\theta '-\theta _c)$$\end{document}. Symbols are defined in Fig. 11
… 
Variation of the dimensionless bedform migration velocity c/u∗′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c/u'_*$$\end{document} with (θ′-θc)/(1-p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\theta '-\theta _c)/(1-p)$$\end{document} for limited sediment supply conditions
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Variation of the dimensionless bedform migration velocity c/u∗′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c/u'_*$$\end{document} with (θ′-θc)/(1-p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\theta '-\theta _c)/(1-p)$$\end{document} for limited sediment supply conditions
… 
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Environmental Fluid Mechanics (2020) 20:1031–1052
https://doi.org/10.1007/s10652-020-09738-6
1 3
ORIGINAL ARTICLE
Bedload transport andbedforms migration undersand
supply limitation
MélanieVah1· ArmelleJarno1· SophieLeBot2· YannFerret2,3· FrançoisMarin1
Received: 4 February 2019 / Accepted: 20 January 2020 / Published online: 31 January 2020
© Springer Nature B.V. 2020
Abstract
Most studies on sediment transport and bedforms migration consider unlimited sediment
supply conditions. However, areas where the sediment supply is limited are common in
coastal and fluvial environments. The present paper, based on physical modelling in a
flume and on a re-analysis of field data obtained in the Eastern English Channel by Ferret
(Morphodynamique des dunes sous-marines en contexte de plate-forme mégatidale (man-
che orientale). approche multi-échelles spatio-temporelles, 2011), considers the effects
of sediment supply limitation on bedload transport and bedforms migration velocity. The
bedload transport is found to be proportional to the fraction of the bed covered by sedi-
ments for a bed exhibiting bedforms. The migration velocity of bedforms depends on the
dominant mode of sediment transport. A new formulation showing a good agreement with
experimental tests and observations in the field is proposed for the dimensionless migra-
tion velocity of these bedforms when sediment transport is dominated by bedload, under
unlimited sediment supply conditions.For limited sediment supply conditions and sedi-
ment transport dominated by bedload, an adaptation of the formulation is suggested from
flume data sets, based on the fraction of the bed covered by sediment.
Keywords Bedload transport· Bedforms· Migration velocity· Coastal zone· Sand supply
limitation· Physical modelling
* François Marin
francois.marin@univ-lehavre.fr
Mélanie Vah
melanie.vah@univ-lehavre.fr
Armelle Jarno
jarnoa@univ-lehavre.fr
Sophie Le Bot
sophie.lebot@univ-rouen.fr
Yann Ferret
yann.ferret@shom.fr
1 UNIHAVRE, CNRS, LOMC, Normandie Univ, 76600LeHavre, France
2 UNIROUEN, UNICAEN, CNRS, Normandie Univ, M2C, 76000Rouen, France
3 Present Address: SHOM, 13, rue du Chatellier, CS92803,29228BrestCedex2, France
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... As sediments generally exhibit size heterogeneity, some authors, e.g., [3,4], have considered the impact of such heterogeneity on transport. The sediment supply may be limited [5]. Despite numerous previous works, our understanding of the physical processes governing sediment transport in the coastal zone is still incomplete. ...
... Tuijnder and Ribberink [18] have shown that bedload transport is significantly dependent on the proportion of the bed covered with sediment in this case. Vah et al. [5] suggested using Equation (12) for the estimation of bedload transport for limited supply conditions ϕ lim : ...
... Bedforms such as ripples or dunes are common on seabeds [19,20]. From flume data sets, Vah et al. [5] proposed to estimate the dimensionless velocity c/u′ * of bedforms under limited sediment supply conditions, when bedload is the dominant mode of sediment transport, in the following way: ...
Cross-Shore Sediment Transport in the Coastal Zone: A Review
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  • Mar 2024
This paper presents a review of cross-shore sediment transport for non-cohesive sediments in the coastal zone. The principles of sediment incipient motion are introduced. Formulations for the estimation of bedload transport are presented, for currents and combined waves and current flows. A method to consider the effect of sediment heterogeneity on transport, using the hiding–exposure coefficient and hindrance factor, is depicted. Total transport resulting from bedload and transport by suspension is also addressed. New research is encouraged to fill the knowledge gap on this topic.
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... In rivers, parameters such as water depth and limited sediment supply are known to often prevent the dunes from reaching equilibrium (Carling et al., 2000;Claude et al., 2012;. In such cases, dune morphological parameters are modified, notably with a limited dune height and hence a relative elongation of the dune wavelength Mazzuoli et al., 2016;Vah et al., 2020;Venditti et al., 2019). According to flume experiments and field observations, dune shape is also influenced by the mobile sediment layer thickness, a consequence of the sediment supply conditions (Kleinhans and Ten Brinke, 2001;Tuijnder et al., 2009;Tuijnder and Ribberink, 2012;Vah et al., 2020;Venditti et al., 2019). ...
... In such cases, dune morphological parameters are modified, notably with a limited dune height and hence a relative elongation of the dune wavelength Mazzuoli et al., 2016;Vah et al., 2020;Venditti et al., 2019). According to flume experiments and field observations, dune shape is also influenced by the mobile sediment layer thickness, a consequence of the sediment supply conditions (Kleinhans and Ten Brinke, 2001;Tuijnder et al., 2009;Tuijnder and Ribberink, 2012;Vah et al., 2020;Venditti et al., 2019). As such, established a conceptual model from experiments in a flume, based on the transport parameter (derived from grain size and flow velocity) and mobile layer thickness. ...
... This model provides a qualitative description of the evolution of dune shape with varying sediment supply. Moreover, on the basis of numerical models (Colombini and Stocchino, 2011), experimental studies (Dreano et al., 2010;Tuijnder et al., 2009;Tuijnder and Ribberink, 2012;Vah et al., 2020) and field case studies (Amos et al., 2004;Carling et al., 2000;Kleinhans and van Rijn, 2002;van Landeghem et al., 2009), it has been shown that a limited sediment supply directly affects sediment transport and dune migration. ...
View
... Les structures sédimentaires en disponible limité ne sont que très peu étudiées par rapport aux structures sédimentaires en disponible illimité alors que les conditions de disponible sableux limité sont communes à la fois en rivière et en mer. Quelques études expérimentales ont été menées en canaux inclinés représentant des conditions fluviales (TUIJNDER et al., 2009 ;DREANO et al., 2010) et en canal à fond non incliné (VAH et al., 2020). L'objectif de cette étude est de comparer qualitativement et quantitativement les longueurs d'ondes à l'équilibre de séries de tests réalisées avec un disponible sédimentaire variable. ...
... Le nombre de Reynolds est défini par Re=Ud/ν avec U la vitesse moyenne du courant et ν la viscosité cinématique du fluide (ν=1.10 -6 m 2 /s). Le paramètre de Shields sur fond plat est défini tel que θ'= * /((s-1)gD50, avec * la vitesse de frottement au fond dans le cas d'un fond plat et basé sur le diamètre des grains (VAH et al., 2020). Le paramètre de Shields critique pour la mise en mouvement des sédiments, θc, est estimé en utilisant la formulation de Soulsby (SOULSBY, 1997) : θc=0,3/(1+1,2 * )+0,055(1-exp(-0,02 * )), avec * = 1 ⁄ / et g l'accélération de la gravité. ...
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... Numerous researchers have used experimental tests in laboratory flumes with unidirectional, steady and uniform currents (e.g. Bennett and Best, 1995;Best and Kostaschuk, 2002;Vah et al., 2020) to develop empirical relationships between dunes and their controlling environmental variables. ...
... Cheng et al., 2004;Villard and Church, 2005;Bartholdy et al., 2005Bartholdy et al., , 2008, or (2) for exploring the relationship between the field dune migration rates and the empirical/numerical bedload transport rates (e.g. Hoekstra et al., 2004;Kostaschuk et al., 2004;Masselink et al., 2009;Williams et al., 2006;Vah et al., 2020). Because of the difficulties for determining the net sediment transport in coastal environments, few studies have been conducted using field sedimentary measurements over an extended period of time (e.g., Gonzalez and Eberli, 1997;Whitmeyer and FitzGerald, 2008) to gain insight into the net sediment transport patterns and the associated morphological developments. ...
Morphodynamics of intertidal dune field in a mixed wave-tide environment: Case of Baie de Somme in Eastern English Channel
Article
  • Nov 2020
  • MAR GEOL
Understanding the response of the intertidal dunes to the varying hydrodynamic conditions in mixed wave-tide environments is of high complexity. Field measurement is one of the most useful approaches to investigate the dune dynamics at different time (semi-diurnal and lunar cycles) and spatial (dunes and associated superimposed bedforms) scales. High-resolution laser scanner data for five successive surveys over a full neap-spring cycle (27 January – 9 February 2014), together with hydrodynamic measurements, have been explored to investigate the morphodynamics of dunes, their superimposed bedforms and their migration in a mixed wave-tide environment (case of the Baie de Somme, Eastern of the English Channel), by the use of a stochastic-physical coupling approach. The dunes are ~12 m wavelength, 0.4 height and oriented orthogonally to the shoreline with angles varying between - 45° and + 45° corresponding to clockwise and counter-clockwise changes, respectively. A stochastic approach, based on spectral analysis, exhibits a series of morphological defects modulating the dune changes following several scale ranges in response to various energy conditions. Such defects can be classified into four categories: (1) limited structures of ~1.6 m wavelengths locally developed along the dune during flood drainage; (2) small-scale superimposed bedforms of ~3.2 m wavelengths built-up across the dunes after high hydrodynamics and proliferated when the energy deceases; (3) large-scale superimposed bedforms of ~6.4 m resulting from the morphological growth of the smaller bedforms; (4) crestline sinuosity with ~25 m wavelength and induced by changes in the orientation of the dunes when they are exposed to high tide-wave activity. The evolving dune defects over the neap-spring cycle is strongly related to the physical mechanisms of sediment transport supplying the migrating dunes and favorable for their self-organization. The physical study of the migrating dunes with the wave-tide driven sediment transport highlights that the long-dune migration components are significantly important during high-energy episodes with a mean explained variance of 65% of the total migration while they decrease to 32% for moderate wave-tide conditions. Good matches of the cross- and long-migration components with the along-shore and the cross-shore sediment transport quantities are recorded with R2 coefficients higher than 70%. These coefficients increase for the offshore dunes where their morphological response to the time-averaged sediment transport is faster while onshore dunes respond at slower timescales resulting in lower R2 coefficients.
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... Huthnance (1982aHuthnance ( , 1982b implemented scarcity as a non-erodible layer and hypothesized that scarcity was required for equilibrium cross-sections to exist, but later studies with more realistic hydrodynamics (e.g., Roos et al., 2004; showed that this was not the case. Regarding other bedforms, sand scarcity was shown to decrease height and width, increase wavelength and three-dimensionality in shape, and affect the migration rate of tidal (Nnafie et al., 2023;Porcile et al., 2017) and fluvial dunes (Dreano et al., 2010;Endo, 2016;Kleinhans et al., 2002;Tuijnder et al., 2009;Vah et al., 2020). However, these bedforms are driven by flow circulations in the vertical plane (Hulscher, 1996;Paarlberg et al., 2009;Vittori & Blondeaux, 2020) rather than the residual circulations in the horizontal plan that drive tidal sandbanks ( Figure 1). ...
Modeling the Cross‐Sectional Dynamics of Tidal Sandbanks in Sediment‐Scarce Conditions
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Full-text available
  • Apr 2024
Plain Language Summary Sandbanks are large‐scale bodies of sand with rhythmic crests and troughs found in shallow seas. They grow in size due to the interaction of the tidal flow with the sand on the seabed until they eventually reach an equilibrium shape. They may also migrate when the tidal flow is asymmetric. Observations in the North Sea have revealed that sandbanks still exist when sand is scarce, but we do not yet understand how scarcity affects the equilibrium shape and the migration rate. Therefore, we have developed a mathematical model that simulates bank evolution of a small bank until equilibrium under increasingly scarce conditions. We find that sand scarcity leads to lower and slightly narrower sandbanks. The asymmetry of the shape also changes. The cross‐section is skewed towards the direction of a residual current (if present) when sand is readily available, but becomes increasingly symmetric when scarcity increases. Bank shapes may even be skewed in the opposite direction when sand is very scarce. Finally, the migration rate of sandbanks increases when sand becomes scarce, but decreases again when sand becomes very scarce. Our findings help to understand how sand scarcity (naturally or due to extraction) affects future marine sandbank landscapes.
View
... L'écoulement dans ce canal est établi à partir de x = 3,5 m. Les tests réalisés simulent des conditions de disponible illimité (VAH et al., 2020). Quatre essais ont été réalisés pour chacun des sables. ...
View
Calibration‐free image analysis method for grain‐size distribution of small natural sand samples
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  • May 2024
Natural sand samples collected from bedload or suspension transport can be too small to be sieved. However, related transported mass to sediment size is crucial to calibrate sediment transport models. Image analysis technique can be an easy and cheap alternative. The present study proposes a general law valid for natural sand grains and small gravels that statistically relates elongation to flatness of particles and gives after some assumptions on grain shape and orientation of grains at the sieve mesh passage, the closest distribution of mass to sieving technique from images of grains given by a flatbed scanner. The proposed model is based on the hypothesis of an ellipsoidal grain shape and a preferential grain crossing aligned with the sieve diagonal. Any sand either homogeneous or heterogeneous from various origins (fluvial, marine and quarry) can be analysed directly without any further need for calibration.
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A visual method for threshold detection of sediment motion in a flume experiment without human interference
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An experimental investigation of entrainment threshold of sediment grains conducted in a non‐tiltable flume is reported and an original processing method based on image correlation suitable for detection of sediment threshold of motion is presented. Unlike existing visual measurement methods, the proposed method is not affected by the individual judgement of the experimentalists that may strongly impact the estimation of incipient motion. Three entrainment thresholds were exhibited. The method highlighted a first threshold for very low shear stress conditions that was interpreted as a nascent movement threshold. The two other thresholds of motion were related to distinct stages of surface mobility of the bed: one related to bedload threshold and the other to bedforms threshold. Series of tests were first performed to study the sensitivity of the method to different parameters: angle of view of the camera, size of the image and acceleration rate of the linear ramp of flow velocity. A ratio of the image surface and the grain surface equal to 3,000 was found as minimum size to perform reliable estimations of entrainment thresholds for all the sediments in the range of 0.328‐2.648 mm that was tested. It was the only condition for the method to work. Once the method was validated, tests were performed with homogeneous sands and compared to results based on reference‐based and visual methods. The correlation method yields similar values for the bedload threshold as those obtained from reference‐based methods. Thus, it could be an alternative to other methodologies by the simplicity of its implementation, precision, needless for human interference and direct correlation between threshold velocity and bed mobility without extrapolation
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The dynamics of spherical particles resting on a horizontal wall and set into motion by an oscillatory flow is investigated by means of a fully coupled model. Both a smooth wall and a rough wall, the latter being composed of resting particles with a random arrangement and with the same diameter as the moving particles, are considered. The fluid and particle motions are determined by means of direct numerical simulations of Navier–Stokes equations and Newton’s laws, respectively. The immersed boundary approach is used to force the no-slip condition on the surface of the particles. In particular, the process of formation of transverse sediment chains, within the boundary layer but orthogonal to the direction of fluid oscillations, is simulated in parameter ranges matching those of laboratory experiments investigating rolling-grain ripple formation. The numerical results agree with the experimental observations and show that the transverse sediment chains are generated by steady recirculating cells, generated by the interaction of the fluid and particle oscillations.
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The formation and migration of sand ripples in closed conduits: Experiments with turbulent water flows
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The transport of solid particles by a fluid flow is frequently found in nature and industry. Some examples are the transport of sand in rivers and hydrocarbon pipelines. When the shear stresses exerted by a fluid flow on a granular bed remain moderate, some grains are set in motion without fluidizing the bed; the moving grains form a layer, known as bed load, that moves while maintaining contact with the fixed part of the bed. Under bed load conditions, the granular bed may become unstable, generating ripples and dunes. Sand ripples are commonly observed in closed conduits and pipes such as in petroleum pipelines, sewer systems, and dredging lines. Although of importance for many scientific domains and industrial applications, the formation of ripples in closed conduits is not well understood, and the problem is still open. This paper presents an experimental study on the formation and migration of sand ripples under a turbulent closed-conduit flow and bed-load conditions. In our experiments, fully-developed turbulent water flows were imposed over a granular bed of known granulometry in a transparent channel, and bed load took place. For different water flow rates and grain diameters, the growth and migration of bedforms were filmed by a high-definition camera, and a numerical code was developed to determine the wavelength and celerity of the bedforms from the acquired images. The obtained results are compared with published stability analyses.
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