Abstract
By means of a two fluid model, we derive a set of non-linear mode coupling equations for weakly interacting low-frequency electrostatic fluctuations that are driven by a sheared ion velocity flow in a non-uniform dusty plasma embedded in an external magnetic field. The linear instability is re-examined. Furthermore, dipolar vortices are shown to be possible stationary solutions of the non-linear equations governing mode coupling of the ion velocity gradient fluctuations in dusty plasmas. The existence regions in parameter space for the dipolar vortex formation are presented. The relevance of our investigation to astrophysical and space plasmas is discussed.
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