DNS and Reynolds-Stress Modeling of Turbulent Cross Poiseuille-Couette Channel Flow

A systematic study is carried out to examine the Reynolds stress budgets in a cross Poiseuille-Couette channel flow. A streamwise pressure gradient drives Poiseuille motion, while equal-magnitude, opposite wall motions impose a Couette shear perpendicular to the main stream, producing a strongly coupled turbulent field. We perform Direct Numerical Simulations (DNS) at friction Reynolds numbers Re_τ,P = 180, 550 and Re_τ,C = 100, 220. The simulations provide term-by-term data for the Reynolds-stress transport equations — production, turbulent and pressure diffusion, redistribution, and dissipation — serving as a benchmark for assessing Reynolds-Averaged Navier–Stokes (RANS) models. Exact DNS closures are compared with the standard sub-models (diffusion, redistribution, dissipation) used in sub-layer-resolved Full Reynolds-Stress Models (FRSM) and with the mean statistics predicted by an FRSM solver for the same cases. Several serious shortcomings are observed in these sub-models, and their combined effect limits FRSM accuracy in predicting even low-order turbulence moments. FRSM improvements are proposed and tested.