We investigate the formation of subaqueous transverse bedforms in turbulent open channel flow by means of direct numerical simulations with fully-resolved particles. The main goal of the present analysis is to address the question whether the initial pattern wavelength scales with the particle diameter or with the mean fluid height. A previous study (Kidanemariam and Uhlmann, J. Fluid Mech., vol. 818, 2017, pp. 716-743) has observed a lower bound for the most unstable pattern wavelength in the range 75-100 times the particle diameter, which was equivalent to 3-4 times the mean fluid height. In the current paper, we vary the streamwise box length in terms of the particle diameter and of the mean fluid height independently in order to distinguish between the two possible scaling relations. For the chosen parameter range, the obtained results clearly exhibit a scaling of the initial pattern wavelength with the particle diameter, with a lower bound around a streamwise extent of approximately 80 particle diameters. In longer domains, on the other hand, patterns are observed at initial wavelengths in the range 150-180 times the particle diameter, which is in good agreement with experimental measurements. Variations of the mean fluid height, on the other hand, seem to have no significant influence on the most unstable initial pattern wavelength. Furthermore, for the cases with the largest relative submergence, we observe spanwise and streamwise sediment waves of similar amplitude to evolve and superimpose, leading to three-dimensional sediment patterns.
Sea ripples are small-scale bedforms which originate from the interaction of an oscillatory flow with an erodible sand bed. The phenomenon of sea ripple formation is investigated by means of direct numerical simulation in which the sediment bed is represented by a large number of fully-resolved spherical grains. Two sets of parameter values are adopted which are motivated by laboratory experiments on the formation of laminar rolling-grain ripples. The knowledge on the origin of ripples is presently enriched by insights and by providing fluid- and sediment-related quantities that are difficult …
Field and laboratory measurements of suspended sediments over wave ripples show, for time-averaged concentration profiles in semi-log plots, a contrast between upward convex profiles for fine sand and upward concave profiles for coarse sand. Careful examination of experimental data for coarse sand shows a near-bed upward convex profile beneath the main upward concave profile. Available models fail to predict these two profiles for coarse sediments. The 1-DV gradient diffusion model predicts the main upward concave profile for coarse sediments thanks to a suitable $β$(y)-function (where $β$ is …
The movement of subaqueous sediment in laminar shearing flow is numerically investigated by the coupled lattice Boltzmann and discrete element methods. First, the numerical method is validated by comparing the phase diagram proposed by Ouriemi et al. ({\it J. Fluid Mech}., vol. 636, 2009, pp. 321-336). Second, a detailed study on sediment movement is performed for sediment with varying solid volume fractions, and a nonlinear relationship between the normalised thickness of the mobile layer and the normalised fluid flow rate is observed for a densely-packed sediment. Third, an independent inves…
Sediment transport over wave-induced ripples is a very complex phenomenon where available models fail to provide accurate predictions. For coastal engineering applications, the 1-DV advection-diffusion equation could be used with an additional parameter α related to the process of vortex shedding above ripples (Absi, 2010). The aim of this study is to provide simple practical analytical tools. An analytical eddy viscosity profile was validated by DNS data of turbulent channel flows (Absi et al., 2011). In this study, we will show that: (1) the period-averaged eddy viscosity in oscillatory boun…
Granular media are frequently found in nature and in industry and their transport by a fluid flow is of great importance to human activities. One case of particular interest is the transport of sand in open-channel and river flows. In many instances, the shear stresses exerted by the fluid flow are bounded to certain limits and some grains are entrained as bed-load: a mobile layer which stays in contact with the fixed part of the granular bed. Under these conditions, an initially flat granular bed may be unstable, generating ripples and dunes such as those observed on the bed of rivers. In fre…
Pore-resolved direct numerical simulations of turbulent open channel flow are performed comparing the structure and dynamics of turbulence over impermeable rough and smooth walls to a porous sediment bed at permeability Reynolds number ($Re_K$) of 2.6, representative of aquatic beds. Four configurations are investigated; namely, (i) permeable bed with randomly packed sediment grains, (ii) an impermeable-wall with full layer of roughness elements matching the top layer of the sediment bed, (iii) an impermeable-wall with half layer of roughness elements , and (iv) a smooth wall. A double-averagi…
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…
Sand ripples are commonly observed in both nature and industry. For example, they are found on riverbeds and in oil pipelines that transport sand. In both natural and industrial cases, ripples increase friction between the bed and fluid and are related to flooding, high pressure drops, and transients. Ripples appear when sediments are entrained as bed load (a mobile granular layer) and are usually considered to be the result of initial bedforms that eventually saturate. Given the small aspect ratio of the initial bedforms, linear analyses can be used to understand the formation of ripples. Thi…
We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approximately ten times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and so total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and i…
Classical scaling relationships for rheological quantities such as the $μ(J)$-rheology have become increasingly popular for closures of two-phase flow modeling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modeling by using a more realistic sediment composition. We investigate the rheological behavior of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to ten, which corresponds to g…
The coupling of sediment transport with the flow that drives it allows rivers to shape their own bed. Cross-stream fluxes of sediment play a crucial, yet poorly understood, role in this process. Here, we track particles in a laboratory flume to relate their statistical behavior to the self organization of the granular bed they make up. As they travel downstream, the transported grains wander randomly across the bed's surface, thus inducing cross-stream diffusion. The balance of diffusion and gravity results in a peculiar Boltzmann distribution, in which the bed's roughness plays the role of th…
We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a lubrication force for particles in close proximity to another solid object, a normal contact force to prevent particles from overlapping, and a tangential contact force to account for friction. Our model extends the work of previous authors to improve upon the time integration scheme to obtain consistent results for particle-wall collisions. Furthermore, we ac…
We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that was generated by means of fully coupled, grain-resolved direct numerical simulations and experimental measurements reviously published by Aussillous {\it et al.} (J. Fluid Mech., vol. 736, 2013, pp. 594-615). The highly-resolved simulation data allows to compute the stress balance of the suspension in the streamwise and vertical directions and the stress exchange between the fluid and particle phase, which is information needed to infer …
The phenomenon of sediment pattern formation in a channel flow is numerically investigated by performing simulations which resolve all the relevant scales of the problem. The numerical approach employed and the flow configuration considered is identical to our previous study (Kidanemariam and Uhlmann J. Fluid Mech., vol. 750, 2014, R2), the only difference being the length of the computational domain. By successively reducing the streamwise length, the minimum box dimension which accommodates an unstable sediment bed is revealed, thus determining the lower threshold of the unstable modes. For …
Understanding the sediment transport in oscillatory flows is essential to the investigation of the overall sediment budget for coastal regions. This overall budget is crucial for the prediction of the morphological change of coastline in engineering applications. Since the sediment transport in oscillatory flows is dense particle-laden flow, appropriate modeling of the particle interaction is critical. Although traditional two-fluid approaches have been applied to the study of sediment transport in oscillatory flows, the approaches do not resolve the interaction of the particles. Particle-reso…
The role of turbulent large-scale streaks in forming subaqueous sediment ridges on an initially flat sediment bed is investigated with the aid of particle-resolved direct numerical simulations of open channel flow at bulk Reynolds numbers up to 9500. The regular arrangement of quasi-streamwise ridges and troughs at a characteristic spanwise spacing between 1 and 1.5 times the mean fluid height is found to be a consequence of the preferential spanwise organization of turbulence in large-scale streamwise velocity streaks. Sediment ridges predominantly appear in regions of weaker erosion below la…
Sediment transport over an erodible sediment bed is studied by particle resolved simulations with a hybrid parallel approach. To overcome the challenges of load imbalance in the traditional domain decomposition method when encountering highly uneven distributions of particles in sediment transport, the parallel approach of Darmana et al.(2006) originally developed for point particle simulations is modified and implemented into particle resolved simulations. A novel memory optimization technique is proposed to reduce the memory requirement of the hybrid approach for spherical particles with equ…
We present results of direct numerical simulation of incompressible fluid flow over a thick bed of mobile, spherically-shaped particles. The algorithm is based upon the immersed boundary technique for fluid-solid coupling and uses a soft-sphere model for the solid-solid contact. Two parameter points in the laminar flow regime are chosen, leading to the emergence of sediment patterns classified as `small dunes', while one case under turbulent flow conditions leads to `vortex dunes' with significant flow separation on the lee side. Wavelength, amplitude and propagation speed of the patterns extr…
This manuscript proposes an analytical model and a simple experimental methodology to estimate the effective settling velocity of very fine sediments at high concentrations. A system of two coupled ordinary differential equations for the time evolution of the bed height and the suspended sediment concentration is derived from the sediment mass balance equation. The solution of the system depends on the settling velocity, which can be then estimated by confronting the solution with the observations from laboratory experiments. The experiments involved measurements of the bed height in time usin…
We examine the drag experienced by a pair of vertical rods moving in tandem through a granular bed immersed in a fluid as a function of their separation distance and speed. As in Newtonian fluids, the net drag experienced by the rods initially increases with distance from the value for a single rod before plateauing to twice the value. However, the drag acting on the two rods is remarkably different, with the leading rod experiencing roughly similar drag compared to a solitary rod, while the following rod experiences far less drag. The anomalous relationship of drag and the distance between th…
Three-dimensional sand ripples can be observed under steady liquid flows in both nature and industry. Some examples are the ripples observed on the bed of rivers and in petroleum pipelines conveying sand. Although of importance, the formation of these patterns is not completely understood. There are theoretical and experimental evidence that aquatic ripples grow from two-dimensional bed instabilities, so that a straight vortex is formed just downstream of their crests. The proposition of Raudkivi (2006), that three-dimensionality has its origin in a vortex instability, is employed here. This p…
The present study revisits the vertical distribution of suspended sediment concentration in an open channel flow with a special attention to sediment diffusion coefficient. If turbulent diffusivity is considered to follow a parabolic-type profile, the diffusivity coefficient is zero at the bed and very small near the bed; so alone it may not be enough to diffuse the particles from bed-load layer to suspension region. Leighton & Acrivos (J. Fluid Mech., vol. 181, 1987, pp. 415-439) introduced the idea of shear-induced diffusion that arises due to the hydrodynamic interactions between solid part…
Experiments are conducted in a laboratory flume on the propagation of a surface wave against unidirectional flow with a sediment bed. This paper presents the spatial variation of bed forms induced by the wave-blocking phenomenon by a suitably tuned uniform fluid flow and a counter-propagating wave. The occurrence of wave-blocking is confirmed by finding a critical wave frequency in a particular flow discharge in which the waves are effectively blocked and is established using the linear dispersion relation. The novelty of this work is to identify the wave-blocking and its influence on the deve…
Small-scale bed form topographies control hyporheic exchange and biogeochemical processes within aquatic sediments, which ultimately affect water quality and nutrient cycling at the watershed scale. The impact of three-dimensional (3D) and small-scale bed form topographies on hyporheic exchange and solute mixing is investigated in the present work. The effect of bed form morphologies on the development of zones of enhanced reaction rates (i.e., hot spots) is also studied. A computational fluid dynamics model to simulate river flow over bed forms is combined with a subsurface flow and multicomp…
A numerical method based upon the immersed boundary technique for the fluid-solid coupling and on a soft-sphere approach for solid-solid contact is used to perform direct numerical simulation of the flow-induced motion of a thick bed of spherical particles in a horizontal plane channel. The collision model features a normal force component with a spring and a damper, as well as a damping tangential component, limited by a Coulomb friction law. The standard test case of a single particle colliding perpendicularly with a horizontal wall in a viscous fluid is simulated over a broad range of Stoke…
Understanding the fundamental mechanisms of sediment transport, particularly those during the formation and evolution of bedforms, is of critical scientific importance and has engineering relevance. Traditional approaches of sediment transport simulations heavily rely on empirical models, which are not able to capture the physics-rich, regime-dependent behaviors of the process. With the increase of available computational resources in the past decade, CFD-DEM (computational fluid dynamics-discrete element method) has emerged as a viable high-fidelity method for the study of sediment transport.…
Breaching of earthen or sandy dams/dunes by overtopping flow and waves is a complicated process with strong, unsteady flow, high sediment transport, and rapid bed changes in which the interactions between flow and morphology should not be ignored. This study presents a depth-averaged two-dimensional (2D) coupled flow and sediment transport model to investigate the flow and breaching processes with and without waves. Bed change and variable flow density are included in the flow continuity and momentum equations to consider the impacts of sediment transport. The model adopts the non-equilibrium …
It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary phase. We investigate the linear stability properties of these systems in considerable generality. Naive formulations of the morphodynamics, featuring exchange of sediment between a well-mixed suspended load and the bed, lead to mathematically ill-posed governing equations. This is traced to a singularity in the linearised system at Froude number $Fr = 1$ that causes unbounded unstable growth of short-wave…
The river bar instability is revisited, using a hydrodynamical model based on Reynolds averaged Navier-Stokes equations. The results are contrasted with the standard analysis based on shallow water Saint-Venant equations. We first show that the stability of both transverse modes (ripples) and of small wavelength inclined modes (bars) predicted by the Saint-Venant approach are artefacts of this hydrodynamical approximation. When using a more reliable hydrodynamical model, the dispersion relation does not present any maximum of the growth rate when the sediment transport is assumed to be locally…
A volume-filtered Euler-Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid-solid slurry flow through a horizontal pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle-particle and particle-wall collisions are modeled using a soft-sphere approach. A se…
The results of Direct Numerical Simulations of the oscillatory flow over a cohesionless bed of spherical particles, mimicking sediment grains, are described. The flow around the sediment particles is explicitly computed by using the immersed boundary method, which allows the force and torque acting on the particles to be evaluated along with their dynamics. Different values of the Reynolds number and different values of the ratio between the grain size and the thickness of the boundary layer are considered such that the results are useful to quantify the sand transport generated by sea waves i…
Here, we propose a conceptual framework of Aeolian sediment transport initiation that includes the role of turbulence. Upon increasing the wind shear stress $τ$ above a threshold value $τ^\prime_t$, particles resting at the bed surface begin to rock in their pockets because the largest turbulent fluctuations of the instantaneous wind velocity above its mean value $\overline{u}$ induce fluid torques that exceed resisting torques. Upon a slight further increase of $τ$, rocking turns into a rolling regime (i.e., rolling threshold $τ_t\simeqτ^\prime_t$) provided that the ratio between the integral…
Fluid dynamics between a particle-laden flow and an evolving boundary are found in various contexts. We numerically simulated the morphodynamics of silica particle deposition from flowing water within geothermal heat exchangers using the arbitrary Lagrangian-Eulerian method. The silica particles were of colloidal size, with submicron diameters, which were primarily transported through the water via Brownian motion. First, we validated the Euler-Euler approach for modelling the transport and deposition of these colloidal particles within a fluid by comparing our simulation results with existing…
In gravel-bed rivers, bedload transport exhibits considerable variability in time and space. Recently, stochastic bedload transport theories have been developed to address the mechanisms and effects of bedload transport fluctuations. Stochastic models involve parameters such as particle diffusivity, entrainment and deposition rates. The lack of hard information on how these parameters vary with flow conditions is a clear impediment to their application to real-world scenarios. In this paper, we determined the closure equations for the above parameters from laboratory experiments. We focused on…
We have studied experimentally particle suspension when injecting a gas at the bottom of an immersed granular layer confined in a Hele-Shaw cell. This work focuses on the dynamics of particles slightly denser than the surrounding fluid. The gas, injected at constant flow-rate, rises through the granular bed then forms bubbles which entrain particles in the above liquid layer. The particles settle down on the edges of the cell, avalanche on the crater formed at the granular bed free surface, and are further entrained by the continuous bubbling at the center. We report the existence of a station…
We study the direction-dependent drag acting on a cylindrical solid intruder with length $L$ and diameter $D$ as it moves in water-saturated granular beds at constant depth. Polysterene and hydrogel grains with diameter $d$ are used to investigate materials which have high contact friction and those which are nearly frictionless, respectively. The drag on the intruder is measured while oriented perpendicular $F_\perp$ and parallel $F_\parallel$ to its axis as a function of speed $U$ from the quasi-static to the rate-dependent regime. We find that the drag anisotropy $ξ= F_\perp/F_\parallel$ is…
Aerodynamic entrainment acts as the pioneer of saltation movement and is critical for understanding the development of aeolian phenomena. Here we performed direct numerical simulations on the aerodynamic lifting of surface particles on a random arranged sediment bed using the discrete element method, and provided evidence that particles do not leave the bed vertically with speeds equal to that needed to reach a height of one grain diameter, as people widely accepted, but with much smaller angles toward the bed surface and much larger velocities. The entrainment rate does not exhibit a quadrati…
CFD-DEM is used to simulate solid-fluid systems. DEM models the motion of discrete particles while CFD models the fluid phase. Coupling both necessitates the calculation of the void fraction and the solid-fluid forces resulting in a computationally expensive method. Additionally, evaluating volume-averaged quantities locally restricts particle to cell size ratios limiting the accuracy of the CFD. To mitigate these limitations, we develop a monolithic finite element CFD-DEM solver which supports dynamically load-balanced parallelization. This allows for more stable, accurate and time efficient …
The problem of determining the threshold of motion of a sediment particle resting on the bed of an open channel has historically been dominated by an approach based on the time-space-averaged bed shear stress (i.e. Shields criterion). Recently, experimental studies have promoted an alternative approach to predict the dislodgement threshold, which is based on the impulse of the flow-induced force. Nonetheless, theoretical analyses accompanying these studies result in complex expressions that fail to provide a direct estimate of said impulse threshold. We employ the work-energy principle to deri…
Saltation models provide considerable insight into near-bed sediment transport. This paper outlines a simple, efficient numerical model of stochastic saltation, which is validated against previously published experimental data on saltation in a channel of nearly horizontal bed. Convergence tests are systematically applied to ensure the model is free from statistical errors emanating from the number of particle hops considered. Two criteria for statistical convergence are derived; according to the first criterion, at least $10^3$ hops appear to be necessary for convergent results, whereas $10^4…
