Boundary-mode-vortex interaction in turbulent channel flow over a non-wavy rough wall

A turbulent model was developed and studied for a high Reynolds number channel flow over a non-wavy rough wall. The non-wavy wall can be rough over a number of finite domains in the streamwise direction., and its shape function is represented in terms of exponential functions with real exponents. The streamwise length-scale of the flow is reduced significantly by an effective rough wall. Asymptotic and scaling analyses are used to determine the leading-order solutions for the wave and the boundary mode due to the non-wavy rough wall. The vortex motion is due to a source term in the system for the vortices. This source term is originated from nonlinear interactions between the wave and the boundary mode components. Due to the roughness elements, more vortices are generated, which can be both of stationary type, due to the rough wall, and of non-stationary type, due to the wave motion. it, is found that the wall roughness affects the wave and the vortex motion through the boundary mode. Certain roughness elements can promote secondary flow instability, which can be enhanced by increasing the roughness amplitude, while some other types of roughness elements can prevent initiation of such flow instability.