Modeling bedform development under turbulent flows using Large-Eddy-Simulation and Immersed-Boundary-Method

Abstract

A numerical model was built to study the mechanism of sedimentary bedform development in hydraulically smooth turbulent flows. The model consisted of a module for flows, a module for sediment transport, and a module for bed surface evolution. The flow was unsteady, three-dimensional and modeled by a Large-Eddy-Simulation (LES) method coupled with an Immersed-Boundary-Method (IBM). Governing equations were discretized on a fixed Cartesian grid by Finite Difference Method. Sediment (bedload) transport was estimated by Van Rijn formula corresponding to bed shear stress distribution obtained from the flow solution. The bed surface evolution was adapted to the sediment flux and described by the Exner–Polya equation. Updated bed surface was then used as the boundary for solving the flow field in the next time step. Time-advancement was discretized by the Adams–Bashforth method. The model was first validated by two test cases of bed shear stress and turbulence statistics over fixed sinusoidal bed surfaces. It was then employed to study initiation and development of bedforms from an initially flat bed to fully developed forms. Formation of newly and successively formed bedforms, growing and downstream propagating process of existing bedforms were very close to experimental observations. Instantaneous bed shear stress and corresponding sediment flux around evolving bedforms, which were difficult to observe in experiments, were also well produced by this model.