On the stability of stratified viscous plane Couette flow. Part 2. Variable buoyancy frequency

Abstract

A statically stable stratification with buoyancy frequency N2(z) = z2 is found to cause large changes in the modal structure for viscous plane Couette flow (as compared with the case when N2(z) = 1) and it also has a strongly destabilizing effect on the flow. On minimizing with respect to both wavenumber and Richardson number, it is found that the flow is unstable if the Reynolds number is greater than about 183. A study of the Reynolds stress and vertical buoyancy flux shows that there is a large transfer of energy from the basic flow to the velocity disturbances and this is consistent with such a surprisingly low value of the minimum critical Reynolds number.