Stratified Plane Couette Flow Research Articles

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

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.

On the stability of visco-elastic liquids in heated plane Couette flow

The stability of thermally stratified plane Couette flow of visco-elastic liquids, with respect to disturbances of small amplitude, is considered. It is found that an initial state of finite elastic stress is necessary for elasticity to effect stability. The critical Rayleigh number of the flow is shown to be decreased for all non-zero rates-of-strain. This greater instability is due solely to the variations of the apparent viscosity with shear rate. In this way, the presence of elasticity can be said to have a destabilizing effect on the flow.