A class of instabilities induced by surface vibrations

This is the authors' abstract. We don't add key points for this paper.

We consider the stability of Couette flow when travelling vibrations perturb one boundary. It is demonstrated that if the bounding surface profile takes the form of sinusoidal waves, then the otherwise stable shear flow becomes unstable for appropriately chosen values of vibration amplitude, phase speed and wavenumber. When instability arises, it is driven by centrifugal forces that are created by wave-imposed changes in the direction of fluid movement. Only subcritical waves, defined as vibrations with phase speed smaller than the maximum flow velocity, cause instability. As the fluid Reynolds number grows, the interval of vibration wavenumbers and phase speeds capable of flow destabilisation is enhanced. A range of parameters is identified for which the vibrations seem to play dual roles: they decrease the flow resistance while simultaneously generating streamwise vortices. This vibration class constitutes an energy-efficient control tool that may potentially intensify the mixing within a flow.