Numerical simulation of turbulent flow over a moving wavy boundary: Norris and Reynolds extended

Abstract

A numerical model of fully developed turbulent channel flow over a moving wavy boundary is presented. The model is of the linear-stability type, employs a transformed coordinate system, and uses the finite difference method for solution. Both the time-independent mean flow and the time-dependent perturbation to the mean flow caused by the traveling wavy boundary are computed. A low-turbulence-Reynolds-number form of the k-epsilon turbulence closure model is employed and three levels of sophistication in modeling the wave-induced Reynolds stresses (in the transformed coordinate system) are introduced. These models are the viscous quasilaminar (VQL) model, the mean eddy viscosity (EV) model, and the full perturbation (FP) model. The model is applied to simulate previous experimental investigations of the flow over wavy boundaries (including a water wave) under a variety of conditions. The solutions generated using both the EV and FP Reynolds stress closure models generally demonstrate very good agreement with the available pressure, stress, velocity, and Reynolds stress experimental data. In contrast, due to its neglect of the perturbation Reynolds stresses, the simple VQL closure model has limited predictive ability, especially for downstream running waves whose wave speed exceeds about half the channel centerline velocity and for cases with low inverse Reynolds numbers (based on the shear velocity and wavelength). For the water wave case, the component of the wave growth rate due to the pressure mechanism predicted by the EV and FP models can be up to three times those of the VQL model in the gravity wave growth range.