Formation of a tripolar vortex in a contaminated electron-positron magnetoplasma with sheared flows

We derive a system of nonlinear equations governing the dynamics of low-frequency electrostatic waves in a magnetized pair plasma with sheared flows that is contaminated by dust grains. For some specific profiles of the equilibrium sheared flows, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. The implications of our investigation to laboratory and space plasmas are discussed.