Turbidity current with a roof: Success and failure of RANS modeling for turbidity currents under strongly stratified conditions

Abstract

Density underflows in general and turbidity currents in particular differ from rivers in that their governing equations do not allow a steady, streamwise uniform “normal” solution. This is due to the fact that density underflows entrain ambient fluid, thus creating a tendency for underflow discharge to increase downstream. Recently, however, a simplified configuration known as the “turbidity current with a roof” (TCR) has been proposed. The artifice of a roof allows for steady, uniform solutions for flows driven solely by gravity acting on suspended sediment. A recent application of direct numerical simulation (DNS) of the Navier-Stokes equations by Cantero et al. (2009) has revealed that increasing dimensionless sediment fall velocity increases flow stratification, resulting in a damping of the turbulence. When the dimensionless fall velocity is increased beyond a threshold value, near-bed turbulence collapses. Here we use the DNS results as a means of testing the ability of three Reynolds-averaged Navier-Stokes (RANS) models of turbulent flow to capture stratification effects in the TCR. Results showed that the Mellor-Yamada and quasi-equilibrium k-ε models are able to adequately capture the characteristics of the flow under conditions of relatively modest stratification, whereas the standard k-ε model is a relatively poor predictor of turbulence characteristics. As stratification strengthens, however, the deviation of all RANS models from the DNS results increases. All are incapable of predicting the collapse of near-bed turbulence predicted by DNS under conditions of strong stratification. This deficiency is likely due to the inability of RANS models to replace viscous dissipation of turbulent energy with transfer to internal waves under conditions of strong stratification. Within the limits of modest stratification, the quasi-equilibrium k-ε model is used to derive predictors of flow which can be incorporated into simpler, layer-averaged models of turbidity currents.