Effects of polarization force on Kelvin-Helmholtz instability in velocity sheared strongly coupled dusty plasma

The effect of polarization force on massive dust grain is studied and the influence of this force is studied on Kelvin-Helmholtz (K-H) instability in magnetized velocity sheared strongly coupled dusty fluid. The ions and electrons are assumed to be thermal and follow Boltzmann distribution and charged dust grains are considered to be strongly coupled. The basic equations are formulated and a modified dispersion relation of K-H instability is obtained with the help of linearized perturbation equations using plane wave perturbations. The effects of sheared flow and polarization force are observed in the modified dispersion relation. We discuss the dispersion relation of K-H instability and derive the condition of K-H instability. The graphical illustrations shows that the polarization interaction parameter and viscoelastic effect have stabilizing on the influence of growth rate of Doppler shifted frequency. A direct numerical approach (Finite Difference Method) is also used to confirm our theoretical solution and we have found good match. The applications of the present work are discussed in astrophysical situation. (author)