Numerical study of plane Couette flow: turbulence statistics and the structure of pressure–strain correlations

Abstract

AbstractThe paper presents the results of direct numerical simulation of turbulent plane Couette flow. The calculations were performed for Reynolds numbers Re =U0H/ν(His the height of the channel, ±U0/2 is the motion velocities of the lower and upper walls, respectively,νis the kinematic viscosity) from 5200 (where viscous effects significantly affect the flow structure) to 80000 (where a logarithmic layer is clearly observed). Estimates of terms of the equation for the balance of turbulent Reynolds stresses are obtained, which indicate the importance of the kinetic energy transport by velocity fluctuations. The vertical transport of the turbulent momentum flux is less important and partly compensated by the transport of pressure fluctuations. It is shown that in the logarithmic layer the normal components of the ‘pressure–strain rate’ correlation tensor are described in the framework of the ‘isotropization of production’ model, and in the central part of the channel they are described by the linear Rotta model [29]. The additive model considering both the interaction of the velocity field fluctuation and the influence of the mean velocity gradient is a good approximation only for the off-diagonal component of the tensor entering the balance equation for the turbulent momentum flux.