Velocity shear effect on the longitudinal wave in a strongly coupled dusty plasma

The characteristics of longitudinal dust acoustic wave (DAW) in presence of velocity shear have been investigated in a strongly coupled dusty plasma using the generalized hydrodynamic (GH) model. In the hydrodynamic regime (ωτm≪1), i.e. when characteristic time τm is slower than inverse of wave frequency, the viscosity in the GH model plays the usual role of wave damping, whereas in the kinetic regime (ωτm≫1), i.e. when characteristic time τm is larger than inverse of wave frequency, viscosity shows energy storing property in the wave. In the kinetic regime, we have studied the longitudinal mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega^{2}=k^{2} (c_{d}^{2}+c_{l}^{2})$\end{document} (where ω is the frequency, k is the wave number, cd is the dust acoustic velocity and cl is the longitudinal velocity that arises due to viscosity) in presence of velocity shear. It is shown that velocity shear can destabilize this mode. Both nonmodal and modal techniques are employed to demonstrate the growth rate of the instability.