Christophe Ancey

Entrainment and motion of coarse particles in a shallow water stream down a steep slope

We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth–death immigration–emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10 %, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.

An exact solution for ideal dam-break floods on steep slopes

Dam-break floods on steep slopes occur in diverse settings. They may result from failure of either natural or man-made dams, and they have been responsible for the loss of thousands of lives [Costa, 1988]. Recent disasters resulting from dam-break floods on steep slopes include those at Fonte Santa mines, Portugal, in November 2006 and Taum Sauk, Missouri, USA, in December 2005. Numerical solutions of the shallow-water equations are generally used to predict the behavior of dam-break floods, but exact analytical solutions suitable for testing these numerical solutions have been available only for floods with infinite volumes, horizontal beds, or both. Computational models used to simulate dam-break floods commonly produce numerical instabilities and/or significant errors close to the moving front when steep slopes and/or irregular terrain are present in the flood path. In part these problems reflect the complex interaction of phenomena not included in model formulation (e.g., intense sediment transport under timedependent flow conditions), but in part they also reflect shortcomings in the numerical solution algorithms themselves. Therefore it is important to obtain exact analytical solutions of the shallow-water equations that can be used to test the robustness of numerical models when they are applied to floods of finite volume on steep slopes. This paper presents a new solution for this purpose.

Front dynamics of supercritical non-Boussinesq gravity currents.

In this paper, we seek similarity solutions to the shallow water (Saint-Venant) equations for describing the motion of a non-Boussinesq, gravity-driven current in an inertial regime. The current is supplied in fluid by a source placed at the inlet of a horizontal plane. Gratton and Vigo (1994) found similarity solutions to the Saint-Venant equations when a Benjamin-like boundary condition was imposed at the front (i.e., nonzero flow depth); the Benjamin condition represents the resisting effect of the ambient fluid for a Boussinesq current (i.e., a small-density mismatch between the current and the surrounding fluid). In contrast, for non-Boussinesq currents the flow depth is expected to be zero at the front in absence of friction. In this paper, we show that the Saint-Venant equations also admit similarity solutions in the case of non-Boussinesq regimes provided that there is no shear in the vertical profile of the streamwise velocity field. In that case, the front takes the form of an acute wedge with a straight free boundary and is separated from the body by a bore.

Rheological interpretation of deposits of yield stress fluids

Abstract Various industrial or natural slurries are coarse, concentrated suspensions with a yield stress. Relevant practical methods are needed to determine the behaviour of such fluids. Here we provide a simple, theoretical approach to describe form of deposits remaining after free surface flow stoppage as a function of fluid characteristics. Thixotropy, inertial effects and sedimentation are neglected. It is demonstrated that the flow depth, as a function of the distance from the edge, can be predicted in any direction. Further analysis shows that there is a clear difference in the form of deposit edge between materials in which there is a grain-to-grain network of interaction and materials in which there is a network of colloidal interaction. These results provide a first order, practical, rheological and structural interpretation of current deposits of pastes, muds, slurries, fresh concrete or magmas.

Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts

Stratification patterns are formed when a bidisperse mixture of large rough grains and smaller more mobile particles is poured between parallel plates to form a heap. At low flow rates discrete avalanches flow down the free surface and are brought to rest by the propagation of shock waves. Experiments performed in this paper show that the larger particles are segregated to the top of the avalanche, where the velocity is greatest, and are transported to the flow front. Here the particles are overrun but may rise to the free surface again by size segregation to create a recirculating coarse-grained front. Once the front is established composite images show that there is a steady regime in which any additional large grains that reach the front are deposited. This flow is therefore analogous to finger formation in geophysical mass flows, where the larger less mobile particles are shouldered aside to spontaneously form static lateral levees rather than being removed by basal deposition in two dimensions. At the heart of all these phenomena is a dynamic feedback between the bulk flow and the evolving particle-size distribution within the avalanche. A fully coupled theory for such segregation–mobility feedback effects is beyond the scope of this paper. However, it is shown how to derive a simplified uncoupled travellingwave solution for the avalanche motion and reconstruct the bulk two-dimensional flow field using assumed velocity profiles through the avalanche depth. This allows a simple hyperbolic segregation theory to be used to construct exact solutions for the particle concentration and for the recirculation within the bulk flow. Depending on the material composition and the strength of the segregation and deposition, there are three types of solution. The coarse-particle front grows in length if more large particles arrive than can be deposited. If there are fewer large grains and if the segregation is strong enough, a breaking size-segregation wave forms at a unique position behind the front. It consists of two expansion fans, two shocks and a central ‘eye’ of constant concentration that are arranged in a ‘lens-like’ structure. Coarse grains just behind the front are recirculated, while those reaching the head are overrun and deposited. Upstream of the wave, the size distribution resembles a small-particle ‘sandwich’ with a raft of rapidly flowing large particles on top and a coarse deposited layer at the bottom, consistent with the experimental observations made here. If the segregation is weak, the central eye degenerates, and all the large particles are deposited without recirculation.

Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport conditions

Even under flow equilibrium conditions, river bed topography continuously evolves with time, producing trains of irregular bed forms. The idea has recently emerged that the variability in the bed form geometry results from some randomness in sediment flux. In this paper, we address this issue by using the Exner equation and a population exchange model derived in an earlier paper. In this model, particle entrainment and deposition are idealized as population exchanges between the stream and the bed, which makes it possible to use birth‐death Markov process theory to track the number of moving grains. The paper focuses on nascent bed forms on initially planar beds, a situation in which the coupling between the stream and bed is weak. In a steady state, the number of moving particles follows a negative binomial distribution. Although this probability distribution does not enter the family of heavy‐tailed distributions, it may give rise to large and frequent fluctuations because the standard deviation can be much larger than the mean, a feature that is not accounted for with classic probability laws (e.g., Hamamori’s law) used so far for describing bed load fluctuations. In the large‐system limit, the master equation of the birth‐death Markov process can be transformed into a Fokker‐Planck equation. This transformation is used here to show that the number of moving particles can be described as an Ornstein‐Uhlenbeck process. An important consequence is that in the long term, the number of moving particles follows a Gaussian distribution. Laboratory experiments show that this approximation is correct when the mean number per unit length of stream,

Yield stress for particle suspensions within a clay dispersion

\vec{N}

Experimental investigation into segregating granular flows down chutes

/L, is sufficiently large (typically two particles per centimeter in our experiments). The particle number fluctuations give rise to bed elevation fluctuations, whose spectrum falls off like

A theoretical framework for granular suspensions in a steady simple shear flow

\omega^{-2}

Solving the Couette inverse problem using a wavelet-vaguelette decomposition

in the high‐frequency regime (with