Kelvin-Helmholtz instability in a weakly coupled dust fluid

We present a non-local linear stability analysis of the shear flow driven Kelvin-Helmholtz (KH) instability in a weakly coupled dusty plasma fluid with particular emphasis on modifications arising from compressibility and dispersive effects. Unlike a neutral hydrodynamic fluid, the effect of compressibility in a dusty plasma originates from finite dust temperature as well as from the finite temperatures of electron and ion fluids which couple to the dust fluid through Coulomb interactions and this feature leads to a much stronger variability of the compressibility effect. Likewise, unlike a neutral fluid, a weakly coupled dust fluid supports compressible dust acoustic perturbations which are dispersive in nature. Our work investigates these issues in detail by carrying out analytical studies for simple forms of shear profiles and exact numerical evaluations for complex shear flows. A perturbative analytic treatment is also presented to elucidate the role of weak compressibility on the KH mode. The nonlinear regime of the instability has also been studied by evolving the equations governing the dynamics of the dusty plasma system. The nonlinear code is first validated against the linear results for the KH mode. Observations on the saturation of the instability in the nonlinear regime and the development of flow patterns during the course of evolution are presented. A comparison of the compressible case with the incompressible case has been provided. (C) 2012 American Institute of Physics. [doi:10.1063/1.3684223]