Neutrally stable wave motions in thermally stratified Poiseuille-Couette flow

The influence of thermal buoyancy on neutral wave modes in Poiseuille-Couette flow is considered. We examine the modifications to the asymptotic structure first described by Mureithi, Denier & Stott [16], who demonstrated that neutral wave modes in a strongly thermally stratified boundary layer are localized at the position where the streamwise velocity attains its maximum value. The present work demonstrates that such a flow structure also holds for Poiseuille-Couette flow but that a new flow structure emerges as the position of maximum velocity approaches the wall (and which occurs as the level of shear, present as a consequence of the Couette component of the flow, is increased). The limiting behaviour of these wave modes is discussed thereby allowing us to identify the parameter regime appropriate to the eventual restabilization of the flow at moderate levels of shear.