Effect of bulk viscosity on Kelvin–Helmholtz instability

An energy functional leading to a resolvable variational problem for determining the critical Reynolds number of laminar-turbulent transition $\mathrm{Re}_{cr}$ is constructed within the framework of the nonlinear energy stability theory of compressible flows. Asymptotic estimates containing the characteristic dependence $\mathrm{Re}_{cr}\sim\sqrt{\alpha+4/3}$ ($\alpha=\eta_b/\eta$) in the main order are obtained for the stability of various modes of Couette compressible gas flow. The asymptotics considered are long-wave approximations. This suggests that the obtained dependence describes the effect of bulk viscosity on the large-scale vortex structures characteristic of Kelvin–Helmholtz instability.