Numerical simulation of sand waves in a turbulent open channel flow

Abstract

We develop a coupled hydro-morphodynamic numerical model for carrying out large-eddy simulation of stratified, turbulent flow over a mobile sand bed. The method is based on the curvilinear immersed boundary approach of Khosronejad et al. (Adv. Water Resour., vol. 34, 2011, pp. 829-843). We apply this method to simulate sand wave initiation, growth and evolution in a mobile bed laboratory open channel, which was studied experimentally by Venditti & Church (J. Geophys. Res., vol. 110, 2005, F01009). We show that all the major characteristics of the computed sand waves, from the early cross-hatch and chevron patterns to fully grown three-dimensional bedforms, are in good agreement with the experimental data both qualitatively and quantitatively. Our simulations capture the measured temporal evolution of sand wave amplitude, wavelength and celerity with good accuracy and also yield three-dimensional topologies that are strikingly similar to what was observed in the laboratory. We show that near-bed sweeps are responsible for initiating the instability of the initially flat sand bed. Stratification effects, which arise due to increased concentration of suspended sediment in the flow, also become important at later stages of the bed evolution and need to be taken into account for accurate simulations. As bedforms grow in amplitude and wavelength, they give rise to energetic coherent structures in the form of horseshoe vortices, which transport low-momentum near-bed fluid and suspended sediment away from the bed, giving rise to characteristic 'boil' events at the water surface. Flow separation off the bedform crestlines is shown to trap sediment in the lee side of the crestlines, which, coupled with sediment erosion from the accelerating flow over the stoss side, provides the mechanism for continuous bedform migration and crestline rearrangement. The statistical and spectral properties of the computed sand waves are calculated and shown to be similar to what has been observed in nature and previous numerical simulations. Furthermore, and in agreement with recent experimental findings (Singh et al., Water Resour. Res., vol. 46, 2010, pp. 1-10), the spectra of the resolved velocity fluctuations above the bed exhibit a distinct spectral gap whose width increases with distance from the bed. The spectral gap delineates the spectrum of turbulence from the low-frequency range associated with very slowly evolving, albeit energetic, coherent structures induced by the migrating sand waves. Overall the numerical simulations reproduce the laboratory observations with good accuracy and elucidate the physical phenomena governing the interaction between the turbulent flow and the developing mobile bed.

Reply to Comment by Sookhak Lari, K. and Davis, G. B. on “ ‘Large Eddy Simulation of Turbulence and Solute Transport in a Forested Headwater Stream’: Invalid Representation of Scalar Transport by the Act of Diffusion”

“…It should be acknowledged that in the published article we (1) mistakenly used the same symbols for the dynamic viscosity of water and the molecular diffusion coefficient of the scalar, (2) neglected to include the value used for the molecular diffusion, and (3) did not mention that σ * is the reciprocal of the turbulent Schmidt number. Although these details should have been included, these omissions do not change well‐established facts that in turbulent flows the mixing of the solute by molecular diffusion is many orders of magnitude less important than that induced by turbulent eddies (Chawdhary et al, ; Chou & Fringer, ; Gualtieri et al, ; Gualtieri & Bombardelli, ; Khosronejad & Sotiropoulos, ; Scalo et al, ). As we mentioned in Khosronejad et al (), the viscous sublayer in Eagle Creek was not resolved in our simulations, as the first node away from the solid boundaries in wall units was (on average) equal to z + = 45 (see Table 3 in Khosronejad et al, ).…”

Large eddy simulation of turbulence and solute transport in a forested headwater stream

“…The volume fraction of conservative tracer ( ψ ) is modeled as a passive scalar whose transport is governed by the following convection‐diffusion equation [ Chou and Fringer , , ; Kraft et al , ; Khosronejad and Sotiropoulos , ]: where σ ∗ is the Schmidt number (= 0.75) [ Khosronejad et al , ] and μ t is the eddy viscosity obtained from LES model [ Kang and Sotiropoulos , ].…”

“…The details of the numerical method for solving the flow, solute transport, and turbulence closure governing equations in complex domains have already been documented extensively elsewhere [ Ge and Sotiropoulos , ; Borazjani et al , ; Kang et al , ; Khosronejad and Sotiropoulos , ], and only a brief summary of key elements of the method will be given here. The governing equations for resolved flow field are discretized in space on a hybrid staggered/nonstaggered grid arrangement [ Gilmanov and Sotiropoulos , ; Ge and Sotiropoulos , ] using second‐order accurate central differencing for the convective terms along with second‐order accurate, three‐point central differencing for the divergence, pressure gradient, and viscous‐like terms.…”

“…In another study VSL3D was employed to underscore the limitations of isotropic RANS models for resolving the structure of secondary flows in natural bends and demonstrate the need for LES. More recently, the VSL3D has been further extended to incorporate free surface effects [ Kang and Sotiropoulos , ] and also develop a coupled hydrodynamic formulation for simulating sand wave dynamics across a range of scales [ Khosronejad et al , , ; Khosronejad and Sotiropoulos , ].…”

Three‐Dimensional Flow Above River Bedforms: Insights From Numerical Modeling of a Natural Dune Field (Río Paraná, Argentina)

“…Numerical models have been used to simulate the interaction of bedforms and hydrodynamics (El Kheiashy et al, ; Khosronejad & Sotiropoulos, ; Lefebvre, Paarlberg, & Winter, ; Omidyeganeh & Piomelli, ; Stoesser et al, ). They compensate for limitations in field and flume measurements as they allow simulations of high‐resolution near‐bed flow fields, provide estimate of turbulence, and can be used with a variety of boundary conditions.…”