Effects of diffusion in the asymptotics of perturbations in stratified shear flow Available to Purchase

Analysis of perturbations in unbounded stratified shear flow is investigated both by integral transforms and by a more general solution given by Lord Kelvin [Philos. Mag. 24(5), 188 (1887)] that is possible for a constant mean shear flow. The latter solution is also valid for the full nonlinear problem and represents an exact solution of the Navier–Stokes equations. Diffusion of momentum and mass or heat are included subject to the Boussinesq approximation and it is concluded that (a) the asymptotic time behavior in the inviscid problem is only valid immediately after the initial moment, (b) diffusion of heat can cause destabilization whereas mass diffusion is stabilizing, and (c) viscosity, no matter how small, dominates the final period with decay ultimately being exponential and independent of the Richardson number.