A Class of Instabilities Induced by Surface Vibrations*

Analysis of the Couette flow response to a bounding plate's vibrations has been carried out. Vibrations in the form of sinusoidal waves characterized by amplitude, wave number, and phase speed have been considered. It is shown that such vibrations can produce instability, giving rise to secondary flow in the form of streamwise vortices. This instability is driven by centrifugal forces created by wave-imposed changes in the direction of fluid movement. The waves cannot be too fast and too slow, too long and too short, and must have a sufficient amplitude to produce instability; relevant bounds have been given. Only subcritical waves, i.e., waves with phase speed smaller than the maximum flow velocity, can produce instability. An increase in the Reynolds number increases the range of vibration wave numbers and phase speeds capable of flow destabilization. A range of parameters has been found where vibrations decrease the flow resistance and, at the same time, produce streamwise vortices. Such vibrations represent an energy-efficient flow control tool for mixing intensification.