A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers

TLDR

The study numerically integrates the three‑dimensional primitive equations for turbulent plane Poiseuille flow at very large Reynolds numbers using a 6720‑point uniform grid and eddy‑viscosity sub‑grid modeling proportional to local velocity deformation, while examining the turbulence energy balance including vertical pressure diffusion and kinetic energy transport. Computed statistics agree with Laufer’s measurements from good to marginal, revealing that only the longitudinal u‑component eddies are downstream‑elongated while v‑eddies exhibit distinct downstream tilts, and the authors conclude the approach is profitable with further accuracy attainable by modest grid refinement.

Abstract

The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with sub-grid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only the u -component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateral v eddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy. It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.