Double structures of steady streaming in the oscillatory viscous flow over a wavy wall

Abstract

The steady streaming induced by oscillatory viscous flow of small amplitudes over a wavy wall has been analysed, and the computed flow patterns have been found to agree well with the flow patterns visualized experimentally in a tube. When the first parameter, α/δ (the ratio of the wavelength of the wavy wall to the thickness of Stokes layer), becomes larger than about 26, the streaming has a double structure consisting of regions of upper and lower pairs of recirculations. As the second parameter, L/δ (the ratio of the amplitude of the wavy wall to the thickness of Stokes layer), is increased, the upper pair of recirculations squeezes in a gap between the lower recirculations above the troughs of the wall. A similar double structure of steady streamings was also observed above ripple marks formed under oscillatory viscous flow. A bearing is suggested of this phenomenon on the determination of stationary profiles of ripple marks.