Shear flow instability in a strongly coupled dusty plasma.

Linear stability analysis of strongly coupled incompressible dusty plasma in presence of shear flow has been carried out using the generalized hydrodynamical (GH) model. With the proper Galilean invariant GH model, a nonlocal eigenvalue analysis has been done using different velocity profiles. It is shown that the effect of elasticity enhances the growth rate of shear flow driven Kelvin- Helmholtz (KH) instability. The interplay between viscosity and elasticity not only enhances the growth rate but the spatial domain of the instability is also widened. The growth rate in various parameter space and the corresponding eigenfunctions are presented.