Wavelength selection and symmetry breaking in orbital wave ripples

Sand ripples formed by waves have a uniform wavelength while at equilibrium and develop defects while adjusting to changes in the flow. These patterns arise from the interaction of the flow with the bed topography, but the specific mechanisms have not been fully explained. We use numerical flow models and laboratory wave tank experiments to explore the origins of these patterns. The wavelength of “orbital” wave ripples (λ) is directly proportional to the oscillating flow's orbital diameter (d), with many experimental and field studies finding λ/d ≈ 0.65. We demonstrate a coupling that selects this ratio: the maximum length of the flow separation zone downstream of a ripple crest equals λ when λ/d ≈ 0.65. We show that this condition maximizes the growth rate of ripples. Ripples adjusting to changed flow conditions develop defects that break the bed's symmetry. When d is shortened sufficiently, two new incipient crests appear in every trough, but only one grows into a full-sized crest. Experiments have shown that the same side (right or left) wins in every trough. We find that this occurs because incipient secondary crests slow the flow and encourage the growth of crests on the next flank. Experiments have also shown that when d is lengthened, ripple crests become increasingly sinuous and eventually break up. We find that this occurs because crests migrate preferentially toward the nearest adjacent crest, amplifying any initial sinuosity. Our results reveal the mechanisms that form common wave ripple patterns and highlight interactions among unsteady flows, sediment transport, and bed topography.National Science Foundation (U.S.) (Award EAR-1225865)National Science Foundation (U.S.) (Award EAR-1225879

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A double-distribution-function lattice Boltzmann method for bed-load sediment transport

The governing equations of bed-load sediment transport are the shallow water equations and the Exner equation. To embody the advantages of the lattice Boltzmann method (e.g., simplicity, efficiency), the three-velocity (D1Q3) and five-velocity (D1Q5) double-distribution-function lattice Boltzmann models (DDF-LBMs), which can present the numerical solution for one-dimensional bed-load sediment transport, are proposed here based on the quasi-steady approach. The so-called DDF-LBM means we use two distribution functions to describe the movement of the two components, respectively. By using the Chapman–Enskog expansion, the governing equations can be recovered correctly from the DDF-LBMs. To illustrate the efficiency of these, two benchmark tests are used, and excellent agreements between the numerical and analytical solutions are demonstrated. In addition, we show that the D1Q5 DDF-LBM has better accuracy compared to the Hudson’s method

A fully Eulerian multiphase model of windblown sand coupled with morphodynamic evolution: Erosion, transport, deposition, and avalanching

Abstract Modeling unsteady windblown sand dynamics requires not only treatment of the sand present in the air as a suspended constituent of a mixture but also consideration of erosion and sedimentation phenomena and consequently of the morphodynamic evolution of the sand-bed surface, including avalanching, especially in the presence of natural or human-built obstacles, artifacts, and infrastructures. With this aim in mind, we present a comprehensive multiphase model capable of accurately simulating all the physical phenomena mentioned above, producing satisfactory results, with reasonable computational effort. As test cases, two- and three-dimensional simulations of dune evolution are reported, as is windblown sand transport over a straight vertical wall. Examples of sand transport around other obstacles are given to show the flexibility of the model and its usefulness for such engineering applications

prediction of mean and turbulent kinetic energy in rectangular shallow reservoirs

AbstractShallow rectangular reservoirs are common structures in urban hydraulics and river engineering. Despite their simple geometries, complex symmetric and asymmetric flow fields develop in such reservoirs, depending on their expansion ratio and length-to-width ratio. The original contribution of this study is the analysis of the kinetic energy content of the mean flow, based on UVP velocity measurements carried throughout the reservoir in eleven different geometric configurations. A new relationship is derived between the specific mean kinetic energy and the reservoir shape factor. For most considered geometric configurations, leading to four different flow patterns, the experimentally observed flow fields and mean kinetic energy contents are successfully reproduced by an operational numerical model based on the depth-averaged flow equations and a two-length-scale k- turbulence closure. The analysis also highlights the better performance of this depth-averaged k- model compared to an algebraic turbu..

Lattice Boltzmann simulations of environmental flow problems in shallow water flows

The lattice Boltzmann method (LBM) proposed about decades ago has been developed and applied to simulate various complex fluids. It has become an alternative powerful method for computational fluid dynamics (CFD). Although most research on the LBM focuses on the Navier-Stokes equations, the method has also been developed to solve other flow equations such as the shallow water equations. In this thesis, the lattice Boltzmann models for the shallow water equations and solute transport equation have been improved and applied to different flows and environmental problems, including solute transport and morphological evolution. In this work, both the single-relaxation-time and multiple-relaxation-time models are used for shallow water equations (named LABSWE and LABSWEMRT, respectively), and the large eddy simulation is incorporated into the LABSWE (named LABSWETM) for turbulent flow. The capability of the LABSWETM was firstly tested by applying it to simulate free surface flows in rectangular basins with different length -width ratios, in which the characteristics of the asymmetrical flows were studied in details. The LABSWEMRT was then used to simulate the one- and two-dimensional shallow water flows over discontinuous beds. The weighted centred scheme for force term, together with the bed height for a bed slope, was incorporated into the model to improve the simulation of water flows over a discontinuous bed. The resistance stress was also included to investigate the effect of the local head loss caused by flows over a step. Thirdly, the LABSWEMRT was extended to simulate a moving body in shallow water. In order to deal with the moving boundaries, three different schemes with second-order accuracy were tested and compared for treating curved boundaries. An additional momentum term was added to reflect the interaction between the following fluid and the solid, and a refilled method was proposed to treat the wetted nodes moving out from the solid nodes. Fourthly, both LABSWE and LABSWEMRT were used to investigate solute transport in shallow water. The flows are solved using LABSWE and LABSWEMRT, and the advection-diffusion equation for solute transport was solved with a LBM-BGK model based on the D2Q5 lattice. Three cases: open channel flow with a side discharge, shallow recirculation flow and flow in a harbour, were simulated to verify the methods. In addition, the performance of LABSWEMRT and LABSWE were compared, and the results showed that the LABSWMRT has better stability and can be used for flow with high Reynolds number. Finally, the lattice Boltzmann method was used with the Euler-WENO scheme to simulate morphological evolution in shallow water. The flow fields were solved by the LABSWEMRT with the improved scheme for the force term, and the fifth order Euler-WENO scheme was used to solve the morphological equation to predict the morphological evolution caused by the bed-load transport

Cell-Based Multi-Parametric Model of Cleft Progression during Submandibular Salivary Gland Branching Morphogenesis

Cleft formation during submandibular salivary gland branching morphogenesis is the critical step initiating the growth and development of the complex adult organ. Previous experimental studies indicated requirements for several epithelial cellular processes, such as proliferation, migration, cell-cell adhesion, cell-extracellular matrix (matrix) adhesion, and cellular contraction in cleft formation; however, the relative contribution of each of these processes is not fully understood since it is not possible to experimentally manipulate each factor independently. We present here a comprehensive analysis of several cellular parameters regulating cleft progression during branching morphogenesis in the epithelial tissue of an early embryonic salivary gland at a local scale using an on lattice Monte-Carlo simulation model, the Glazier-Graner-Hogeweg model. We utilized measurements from time-lapse images of mouse submandibular gland organ explants to construct a temporally and spatially relevant cell-based 2D model. Our model simulates the effect of cellular proliferation, actomyosin contractility, cell-cell and cell-matrix adhesions on cleft progression, and it was used to test specific hypotheses regarding the function of these parameters in branching morphogenesis. We use innovative features capturing several aspects of cleft morphology and quantitatively analyze clefts formed during functional modification of the cellular parameters. Our simulations predict that a low epithelial mitosis rate and moderate level of actomyosin contractility in the cleft cells promote cleft progression. Raising or lowering levels of contractility and mitosis rate resulted in non-progressive clefts. We also show that lowered cell-cell adhesion in the cleft region and increased cleft cell-matrix adhesions are required for cleft progression. Using a classifier-based analysis, the relative importance of these four contributing cellular factors for effective cleft progression was determined as follows: cleft cell contractility, cleft region cell-cell adhesion strength, epithelial cell mitosis rate, and cell-matrix adhesion strength

A finite volume shock-capturing solver of the fully coupled shallow water-sediment equations

This paper describes a numerical solver of well-balanced, 2D depth-averaged shallow water-sediment equations. The equations permit variable variable horizontal fluid density and are designed to model watersediment flow over a mobile bed. A Godunov-type, HLLC finite volume scheme is used to solve the fully coupled system of hyperbolic conservation laws which describe flow hydrodynamics, suspended sediment transport, bedload transport and bed morphological change. Dependent variables are specially selected to handle the presence of the variable density property in the mathematical formulation. The model is verified against analytical and semi-analytical solutions for bedload transport and suspended sediment transport, respectively. The well-balanced property of the equations is verified for a variable-density dam break flow over discontinuous bathymetry. Simulations of an idealised dam-break flow over an erodible bed are in excellent agreement with previously published results ([1]), validating the ability of the model to capture the complex interaction between rapidly varying flow and an erodible bed and validating the eigenstructure of the system of variable-density governing equations. Flow hydrodynamics and final bed topography of a laboratory-based 2D partial dam breach over a mobile bed are satisfactorily reproduced by the numerical model. Comparison of the final bed topographies, computed for two distinct sediment transport methods, highlights the sensitivity of shallow water-sediment models to the choice of closure relationships