Session U06: Geophysical Fluid Dynamics: Sediment Transport (8:45am - 9:30am CST)

Mass exchange in barchan-barchan interactions

Barchan dunes grow under one-directional fluid flow and limited amount of granular material. They are usually organized in barchan fields, where dune interactions control the behavior of the entire field. In a previous study [Assis and Franklin, Geophys. Res. Lett., submitted], we investigated barchan-barchan interactions in the subaqueous case and found five different patterns for both aligned and off-centered bedforms. We proposed maps of patterns that depend on the ratio between the number of grains of each dune, Shields number and bedform alignment. We now investigate the barchan-barchan interactions at the grain scale. For that, experiments were conducted in a water channel of transparent material where controlled grains were poured inside, forming pairs of granular piles in both aligned and off-centered configurations. A high-speed camera placed above the channel acquired images of the bedforms, and with image processing we tracked several of the moving grains. We obtained the exchange of grains between barchans (including barchan-barchan collisions). The present results are crucial to understand how different patterns emerge from barchan-barchan interactions.   

Influence of the initial volume fraction on the collapse of submerged granular columns

Gravity-driven flows of granular materials are encountered in numerous natural phenomena such as debris flows and landslides, as well as in various processes in the chemical, food and pharmaceutical industries. In this presentation, we present simulations of the collapse of a granular column, submerged in water, under its own weight. Our study is based on a two-velocity, two-pressure Eulerian model that takes into account compaction, dilatancy and the complex rheological behavior of the granular phase. This model is treated numerically using a predictor-corrector time-integration scheme, coupled with a projection method for the computation of phasial pressures. In the simulation presented herein, emphasis is placed on the different behaviours that are observed depending on whether the initial packing is loose or dense, exhibiting contractancy or dilatancy respectively. The role of the ambient fluid is also highlighted by a comparison between dry and submerged columns.   

Mathematical modeling of erosion and sedimentation in networks

Erosion and sedimentation, in the environmental context, is represented as the evolution of solid bodies due to the forces exerted by the fluid or air on the contact surface, which both often lead to reconfiguration and change of the topology of the geological structures and porous media. These processes are notably very complicated and challenging to study in reality. In this work, we formulate novel and idealized mathematical models to examine the internal evolution of flow-networks in the setting of cylindrical channels, undergoing a unidirectional flow, by using asymptotic and numerical techniques. Starting from the Stokes equations combined with an advection-diffusion solid transport, we propose a model to construct a complete analysis of both the erosion and sedimentation in geological structures and porous media. The considered approach is of the form of threshold laws: the fluid-solid interface erosion and sedimentation occur when the total shear stress is, respectively, greater and lower than some specific critical values, depending on the solid material. As a consequence of the erosion and sedimentation, the structure channels' radii expand and shrink respectively.   

The big picture of barchan-barchan interactions

Barchans are crescent-shaped dunes that are often organized in barchan fields, where binary interactions play a significant role in regulating their dynamics and sizes. We investigate experimentally the different types of interactions occurring between two barchans and which physical aspects govern them. The experiments were conducted in a water channel of transparent material where controlled grains were poured inside, forming pairs of granular piles in both aligned and staggered configurations. For each test, a given water flow was imposed, forming a pair of barchans that interacted differently depending on the tested conditions. In our experiments, different grain types (diameter and density), pile masses, distances and water flow rates were used, and a high-definition camera acquired images of the bedforms. As a result, five different patterns were identified for each configuration (aligned or staggered), for which we propose pattern maps that depend on the ratio between the number of grains of each dune and the Shields number. Our results shed light on the size regulation of barchans in a dune field.   

Motion of grains within a barchan dune

A one-directional fluid flow acting over a granular bed with a low sediment supply can produce crescent-shaped dunes. These bedforms, called barchans, are characterized by their tips pointing downstream and are frequently found in nature and industrial applications. Though they have been studied over decades, many aspects related to their dynamics are still under debate, so that a crucial aspect to understand these dunes is to obtain data at the grain scale. Numerical simulations can provide information of this type, which is difficult to measure through experiments. In this work, by employing the computational fluid dynamics - discrete element method, we present measurements at the grain scale of barchan dunes formed by the action of a water flow in turbulent regime over a granular pile with an initial conical shape. The simulations captured well the particle's trajectories, displaying remarkable agreement with experiments and allowing quantification of the local granular flux and the resultant force acting on each grain. Our numerical results shed light on the particle motion leading to barchan dunes and raise several questions, such as the possibility of applying this methodology to dunes consisting of non-spherical grains as occur in nature.   

Direct numerical simulations of bedload transport over inclined particle beds

We present results from open-channel, Euler-Lagrange direct numerical simulations of turbulent flow over an erodible particle bed. A total of 31 simulations are conducted. The shear Reynolds number is kept fixed at $Re_{\tau}=180$, while the Shields to critical Shields ratio $\theta/\theta_{cr}$ and the bed inclination angle $\beta$ varied in the range 1.32 to 4.04 and $-30^{\circ}$ to $30^{\circ}$, respectively. For the $\beta=0$ cases, we find our results to be in good agreement with the Wong & Parker (WP) (2006) correction of Meyer-Peter and M{\"u}ller (1948) bedload transport relation. Consequently, we use the sediment flux values from the non-horizontal simulations to propose a correction to the WP model so as to extend it to non-horizontal beds. Additionally, we compute the critical adverse bed inclination angle $\beta_{cr}$ for all $\theta/\theta_{cr}$ considered values. $\beta_{cr}$ represents the angle beyond which the sediment flux points in the direction opposite to the flow. Finally, we extract the streamwise velocity component at the sediment surface and use it to propose an improved Dirichlet boundary condition for Euler-Euler turbulent flow simulations over inclined sediment beds.   

On The Large Fluctuations Of The Local Particle Flux For Bedload Dominated Transport

We present results from open-channel, Euler-Lagrange direct numerical simulations of turbulent flow over an erodible particle bed consisting of 1.3 million particles. All simulations are carried out at the same shear Reynolds number of $Re_{\tau}$ = 180. The particle Reynolds number $Re_p$ and the ratio of Shields number to the critical Shields number $\theta/\theta_{cr}$ varied in the range 11.4 to 29.8 and 1.32 to 5.98, respectively. From a global perspective, our simulations correctly reproduce the Wong \& Parker (2006) (WP) correction of Meyer-Peter \& Muller bedload transport relation with a similar trend in the scatter. On the other hand, from a local and instantaneous perspective, our simulations show that the sediment flux could differ by a few orders of magnitude from WP. We use the resolved flow field and swirling strength $\lambda_{ci}$ to show that, comparing with the particle bed arrangement, the turbulent fluctuations coupled with particle inertia are more responsible for this large scatter. We further extract the bed-tangential and bed-normal components of velocity at the surface of the particle bed. These velocity components, which are essential to the modelling of sediment transport, also demonstrate large variations at the local and instantaneous level.   

Scour, Deposit and Mass Flux Directionality Induced by a Vertical Yawed Permeable Wall

Experiments were conducted to quantify local scour and deposit induced by a rectangular vertical permeable wall in critical mobility condition with the ultimate goal to design hydraulic structures inducing mass flux directionality and controlling fluvial bathymetry. Theoretical scaling for the maximum scour depth is derived from the phenomenological theory of turbulence, based on modeled scour volume and key assumptions on the large-scale velocity in the scour hole, and on the drag force induced by the wall. The theoretical prediction shows satisfactory agreement with experimental results in various installation configurations, e.g. wall porosity, angle, and size. Particular attention is devoted to the asymmetry of the local bathymetry to identify the most effective wall configuration to steer sediment deposit along a desired direction. The installation angle is shown to affect the geometry and maximum depth of the scour and deposit volumes, as well as the spanwise location of the deposit peak and centroid.   

Evaluation of erosion-rate models for numerical simulations of sediment transport

This work investigates the performance of commonly used sediment transport models and high-resolution Navier-Stokes equations solution methods. Entrainment functions predict the average rate of transport of sediment eroded from a channel bed based on the average wall shear stress. However, as computational resources increase, eddy-resolving methods, in which a range of temporal and spatial scales is present, are becoming more widespread. In this work we show that the accuracy of various entrainment functions is compromised when applied instantaneously, as is necessary in Direct Numerical Simulation (DNS), and Large Eddy Simulation (LES). For small values of the wall shear stress (normalized by particle size and density ratio) the fine spatial and temporal resolution of wall-resolved simulations can yield overestimation of the sediment transport; methods that yield a more coarse-grained solution, such as wall-modeled large-eddy simulations, result in more accurate predictions. A short-time averaging of the velocity field is shown to improve the performance of the entrainment functions combined with eddy-resolving solution methods.   

Erosion of a granular bed by an oscillating foil

Immersed solid structures oscillating near the surface of a granular bed are encountered in various systems. For instance, the motion of an underwater flapping foil can be used for energy harvesting but modifies locally the sediment transport disturbing the marine life. Indeed, these immersed structures generate complex flow patterns that trigger erosion and transport of particles. To study the coupling between the motion of the foil, the flow generated and the erosion process, we developed a model experiment consisting of a horizontal rigid foil placed above the surface of the granular layer and subjected to vertical periodic oscillations. The oscillations generate vortices, which in turn trigger the erosion of the granular bed. We describe the influence of the different parameters on the onset of erosion. Using PIV measurements, we characterize the periodic vortices generated by the oscillation of the foil. The experimental measurements of the erosion threshold are then rationalized by coupling the fluid flow model and a local erosion criterion. This approach allows us to obtain a general condition that leads to the erosion of the sediment bed based on the motion of the foil.   

Drop impact on an immersed granular bed

Water erosion of natural landscape surfaces is initiated by raindrops penetrating a thin sheet of surface runoff and the underlying granular soil surface. Here, we investigate experimentally the impact of a water drop on an immersed cohesionless granular bed in the presence of a thin, still water layer. We characterize the erosion threshold for varying drop size, water-layer thickness, and substrate particle size. Our experiments reveal two different regimes depending on the ratio between drop diameter and liquid thickness. For a thin film, the deformation of the interface induced by the drop directly lead to the erosion of the granular bed. For sufficiently deep liquid films the impact of the drop is not sufficient to directly trigger the erosion by deforming the free surface but instead generates a vortex ring inside the liquid layer, which triggers the erosion \newline of grains. Coupling the flow generated by the impacting drop with the properties of the grains allows us to describe the erosion threshold and the formation of a suspension during intense rainstorms   

A dynamical model of a quasi-2D dune corridor

Sand dunes often form larger collectives known as dune fields. Notwithstanding significant progress in our understanding of single dune dynamics, the morphology of dune fields is still poorly understood. Previous models abstracted migrating dunes as independent agents colliding with each other, but recent experiments in our laboratory revealed that two subaqueous dunes, one directly upstream of the other, can interact at large distances even if they are not in direct contact. The turbulent fluctuations associated with the wake of the upstream dune enhance sediment flux over the downstream dune and thus increase its migration rate. They also impact the exchange of sediment between neighbouring dunes, which may lead to a dune starvation. Here, we present a data-driven dynamical model of a quasi-2D periodic train of hydrodynamically interacting dunes, which is the first step towards a realistic reduced-complexity model of a dune field that would incorporate the wake-induced feed back. We identify the steady states of the system, probe their stability, and make predictions about the long-time evolution of a quasi-2D dune corridor. We also discuss the stochastic aspects of the dynamics and compare theoretical predictions with the laboratory experiments.   

Using instrumented particles for coarse sediment entrainment studies

Sediment transport processes shaping Earth's surface are important to study and find a range of applications across fields including environmental fluid dynamics and geomorphology. This work introduces an accessible and low cost approach for assessing the initiation of sediment entrainment, a major challenge for earth surface scientists and hydraulic engineering. Specifically, a miniaturized instrumented particle of 3cm in diameter is used for the direct monitoring of destabilisation potential of an open channel flow bed surface comprising of uniform coarse particles [1]. The instrumented particle has been calibrated and used to investigate its probability of entrainment due to turbulent flows, by assessing its entrainment frequency and magnitude, using the logged readings. These are also linked to near bed surface flow hydrodynamics [2,3]. References [1] Al-Obaidi, K.; Xu, Y.; Valyrakis, M. (2020). The Design and Calibration of Instrumented Particles for Assessing Water Infrastructure Hazards, \textit{J. Sens. Actuator Netw.}~\textbf{2020},~9, 3, 36, 1-18, https://doi.org/10.3390/jsan9030036. [2] Valyrakis, M.; Diplas, P.; Dancey, C.L. Entrainment of coarse particles in turbulent flows: An energy approach. \textit{J. Geophys. Res. Earth Surf}. \textbf{2013}, 118, 42--53, doi:10.1029/2012JF00235. [3] P\"{a}htz, T.; Clark, A. H.; Valyrakis, M.; Duran, O. The Physics of Sediment Transport Initiation, Cessation, and Entrainment Across Aeolian and Fluvial Environments. \textit{Rev. Geophys}. \textbf{2020}, 58, 1, 1-58, doi:10.1029/2019RG000679.   

Study of the plume surface interaction cratering process using stereo photogrammetry

With NASA's renewed interest in returning humans to the Moon through the Artemis program, understanding plume surface interactions (PSI's) has become vital to ensure that future lunar missions are conducted safely and successfully. PSI's encompass the interaction between the rocket plume of a craft landing on the surface and the surface itself. These interactions have a potential to create a crater in the surface and can also lead to a formation of large cloud of particulate around the landing sites. The current work seeks to employ non-intrusive optical diagnostic technique such as stereo photogrammetry for full-domain, three-dimensional measurements of crater geometry during the PSI process. The experiments were carried out on a bench-scale, atmospheric facility with nozzle height taken as a varying parameter. Two high-speed cameras were arranged in stereo configuration which allowed for high spatio-temporal resolution of the crater formation process. Preliminary experiments showed that the dust cloud created from the ejected particles limited the optical access of the crater. Thus, primary focus of this work will be to overcome the challenge associated with applying the current optical diagnostic technique for studying the PSI process.