Boundary wave-vortex interaction in channel flow with a wavy wall at high Reynolds numbers

Abstract

Asymptotic and scaling analyses at high Reynolds numbers are used to investigate channel flow over a wavy wall. Flow is divided into a core away from the boundaries and two viscous wall layers adjacent to the boundaries. The spanwise dependent amplitudes of the Tollmien–Schlichting (TS) and boundary waves contribute to a source term in the system for the longitudinal vortices. The presence of this source term requires streamwise variation of either the TS wave or the boundary wave. For the case where the initial TS wave does not exist, the boundary wave, due to the wavy wall, controls the existence, scales, variations and shape of the longitudinal vortices. For the case where the initial TS wave is present, the wavy wall affects the TS wave and the vortex motion through the boundary wave. The TS wave is subjected to secondary three-dimensional instability for favorable boundary waves due to particular forms of the wavy wall, while the secondary instability can be suppressed by special boundary waves due to some other particular wavy walls.