Eddy Viscosity and Velocity Profiles in Fully-Developed Turbulent Channel Flows

Abstract

In this study, we present eddy viscosity formulations based on analytical solutions for turbulent kinetic energy (TKE) in fully-developed turbulent channel flows. Mean streamwise velocities are obtained by solving the momentum equation with the proposed analytical eddy viscosity formulations. Our results were validated by comparisons with DNS data of fully-developed turbulent channel flows for 300 < Re_τ < 2000 (where Re_τ denotes the friction Reynolds number defined by the friction velocity u_τ, kinematic viscosity ν and the channel half-width δ). Our method allows accurate description of mean streamwise velocity profiles and turbulent shear stress outside the log-law layer, in the viscous and buffer layers and in the outer region. The aim of this study is to provide simple analytical tools for turbulent channel flow applications.