Compressibility effects on a shear flow in strongly coupled dusty plasma. I. A study using computational fluid dynamics

We study compressibility effects on the two-dimensional strongly coupled dusty plasma by means of computational fluid dynamics (CFD) with the Kolmogorov flow as an initial shear flow profile. Nonlinear compressible vortex flow dynamics and other linear and nonlinear properties of such flow in the presence of variable density, pressure, and electrostatic potential are addressed using a generalised compressible hydrodynamic model. The stabilizing effect of compressibility on the unstable shear flows in the presence of strong correlation (⁠$τm>0$⁠) is presented. Increasing the Mach number relatively reduces the growth-rate of perturbation. On the other hand, strong correlation makes the medium to be more unstable and increases the growth rate. Using an eigen value solver, various linear properties of compressible Kolmogorov flow have been investigated for a range of variable parameters, for example, Mach number, Reynolds number, and viscoelastic coefficient (τ_m). Compressible Kolmogorov flow becomes unstable above a critical value of the Reynolds number (R_c), and below R_c, the shear flow is found to be neutrally stable. In this study, it is found that the viscoelasticity reduces the value of R_c. For our choice of parameters, at $τm=τmc$⁠, the compressible Kolmogorov flow becomes unconditionally unstable and no R_c exists for values of τ_m higher than $τmc$⁠. To address the nonlinear properties, for example, mode-mode interaction due to the presence of nonlinearity in the fluid, vortex formation, etc., a massively parallelized Advanced Generalized SPECTral Code (AG-Spect) has been developed. AG-Spect, a newly developed code, is an efficient tool to solve any set of nonlinear fluid dynamic equations. A good agreement in linear growth rates obtained from the eigen value solver and time dependent simulation (AG-Spect) is found. In our CFD study, the suppression of instability, elongated vortex structures, pattern formation, nonlinear saturation, and visco-elastic oscillations in perturbed kinetic energy have been observed for various values of Mach number, Reynolds number and τ_m.