Analytical Solution of Two Gradient-Diffusion Models Applied to Turbulent Couette Flow

Two widely used gradient-diffusion models of turbulence, when applied to fully-developed Couette flow, are shown to reduce to a set of equations that can be solved analytically. The solutions reveal that both models predict the turbulence kinetic energy to be constant across the entire central region in which the modeling is applied. The implications for the prediction of velocity and eddy viscosity are explored. It is found that the point at which the model equations are matched to the near-wall boundary conditions is an important parameter of the solution.