Poiseuille and Couette flows in the transitional and fully turbulent regime

Abstract

We present an extensive compilation of direct numerical simulation (DNS) data for Poiseuille and Couette flows, from the laminar into the fully turbulent regime, with the goal of highlighting similarities and differences. The data suggest that, for a given bulk velocity, Couette flow yields less resistance than Poiseuille flow and greater turbulence kinetic energy, which may be beneficial for more efficient diffusion, thus suggesting the effectiveness of fluid transport devices based on moving belts as opposed to classical ducts. Both flows exhibit similar trends for the wall-parallel velocity variances, which increase logarithmically with the Reynolds number. The shear stress and the wall-normal stress tend to saturate faster in Couette flow, which can thus be regarded as a limit to which Poiseuille flow tends, in the limit of high Reynolds number. Excess production over dissipation is found in the outer part of Poiseuille and Couette flow, which is responsible for non-local transfer of energy. However, the structure of the core flow seems to attain an asymptotic state which consists of a parabolic and linear mean velocity profile, respectively, and it seems unlikely that substantial changes to this scenario will occur at Reynolds numbers reachable by DNS in the foreseeable future.