Kolmogorov flow in two dimensional strongly coupled dusty plasma

Undriven, incompressible Kolmogorov flow in two dimensional doubly periodic strongly coupled dusty plasma is modelled using generalised hydrodynamics, both in linear and nonlinear regime. A complete stability diagram is obtained for low Reynolds numbers R and for a range of viscoelastic relaxation time τ_m [0 < τ_m < 10]. For the system size considered, using a linear stability analysis, similar to Navier Stokes fluid (τ_m = 0), it is found that for Reynolds number beyond a critical R, say R_c, the Kolmogorov flow becomes unstable. Importantly, it is found that R_c is strongly reduced for increasing values of τ_m. A critical $τmc$ is found above which Kolmogorov flow is unconditionally unstable and becomes independent of Reynolds number. For R < R_c, the neutral stability regime found in Navier Stokes fluid (τ_m = 0) is now found to be a damped regime in viscoelastic fluids, thus changing the fundamental nature of transition of Kolmogorov flow as function of Reynolds number R. A new parallelized nonlinear pseudo spectral code has been developed and is benchmarked against eigen values for Kolmogorov flow obtained from linear analysis. Nonlinear states obtained from the pseudo spectral code exhibit cyclicity and pattern formation in vorticity and viscoelastic oscillations in energy.