A spectral-like turbulence-resolving scheme for fine sediment transport in the bottom boundary layer

Abstract

A hybrid spectral-compact finite difference scheme for turbulent-resolving simulation of fine sediment transport in the bottom boundary layer is presented. The numerical approach extends an earlier pseudo-spectral model for direct numerical simulation (DNS) of turbulent flows with a sixth-order compact finite difference scheme in the wall-normal direction on Chebyshev grid points. The compact finite difference scheme allows easy implementation of flow-dependent properties (e.g., viscosity, diffusivity and settling velocity) and more flexible boundary conditions while still maintain spectral-like numerical accuracy. The numerical model is verified with analytical solutions of flow velocity and particle concentration of two simple Newtonian rheological closures under laminar condition. Prior laboratory and DNS data of turbulent channel flow are also used to validate the code. Several numerical simulations were carried out in a turbulent channel flow setting to investigate the interplay between the two turbulence modulation mechanisms induced by the presence of sediment, namely sediment-induced density stratification and enhanced viscosity due to rheological stress. We demonstrate that at the Reynolds number, Richardson number, and non-dimensional settling velocity used here, the flow remains turbulent but sediment-induced density stratification already causes noticeable damping of turbulence (drag reduction). By further introducing a Newtonian rheological stress into the system, flow turbulence is further damped by the increased effective viscosity, which can trigger laminarization.