Dust velocity shear driven rotational waves and associated vortices in a nonuniform dusty plasma

We show that an equilibrium dust velocity gradient can generate coupled dust drift-like modes and dust acoustic waves in a nonuniform dusty plasma in which dust grains are under the influence of electrostatic and centrifugal forces. For this purpose, we use Boltzmann distributed electrons and ions as well as the continuity and momentum equations for mobile charged dust grains, and derive a pair of equations which shows nonlinear coupling between the scalar potential and the parallel (to the axis of dust grain rotation due to the centrifugal force) dust fluid velocity. In the linear regime, we find instability of coupled drift-like dust modes and dust acoustic waves. In the nonlinear regime, self-interaction among linearly excited modes produces self-organization in the form of different types of vortices. The relevance of our investigation to laboratory plasmas and space environments is discussed