Numerical simulation of turbulent, plane parallel Couette-Poiseuille flow

Abstract

We present numerical simulation and mean-flow modelling of statistically stationary plane Couette-Poiseuille flow in a parameter space with and, where are independent Reynolds numbers based on the plate speed and the volume flow rate per unit span, respectively. The database comprises direct numerical simulations (DNS) at, wall-resolved large-eddy simulations at, and some wall-modelled large-eddy simulations (WMLES) up to. Attention is focused on the transition (from Couette-type to Poiseuille-type flow), defined as where the mean skin-friction Reynolds number on the bottom wall changes sign at. The mean flow in the plane is modelled with combinations of patched classical log-wake profiles. Several model versions with different structures are constructed in both the Couette-type and Poiseuille-type flow regions. Model calculations of, (the skin-friction Reynolds number on the top wall) and show general agreement with both DNS and large-eddy simulations. Both model and simulation indicate that, as is increased at fixed, passes through a peak at approximately, while increases monotonically. Near the bottom wall, the flow laminarizes as passes through and then re-transitions to turbulence. As increases, increases monotonically. The transition from Couette-type to Poiseuille-type flow is accompanied by the rapid attenuation of streamwise rolls observed in pure Couette flow. A subclass of flows with is investigated. Combined WMLES with modelling for these flows enables exploration of the limit, giving as.