We consider the effect the competing mechanisms of buoyancy-driven acceleration (arising from heating a surface) and streamline curvature (due to curvature of a surface) have on the stability of boundary-layer flows. We confine our attention to vortex type instabilities (commonly referred to as Görtler vortices) which have been identified as one of the dominant mechanisms of instability in both centrifugally and buoyancy driven boundary layers. The particular model we consider consists of the boundary-layer flow over a heated (or cooled) curved rigid body. In the absence of buoyancy forcing the flow is centrifugally unstable to counter-rotating vortices aligned with the direction of the flow when the curvature is concave (in the fluid domain) and stable otherwise. Heating the rigid plate to a level sufficiently above the fluid's ambient (free-stream) temperature can also serve to render the flow unstable. We determine the level of heating required to render an otherwise centrifugally stable flow unstable and likewise, the level of body cooling that is required to render a centrifugally unstableflow stable.

It is well known that buoyancy forces and centrifugal effects can render a flow unstable to longitudinal vortex structures. Such competing instability mechanisms can be found in flows such as the curved mixing layer formed by the passage of two streams of fluid at different temperatures in the wake of a curved body. Via an asymptotic consideration of the problem we are able to characterize the interplay between these mechanisms. We are also able to determine the level of convex curvature required to stabilize unstably stratified mixing layers and the level of concave curvature required to destabilize stably stratified mixing layers.

We consider nonlinear wave motions in thermally stratified Poiseuille flow. Attention is focused on short wavelength wave modes for which the neutral Reynolds number scales as the square of the wave number. The nonlinear evolution of a single monochromatic wave is governed by a first harmonicr mean-flow interaction theory in which the wave-induced mean flow is comparable in size to the wave component of the flow. An integrodifferential equation is derived which governs the normal variation of the wave amplitude. This equation admits finite-amplitude solutions which bifurcate Ž . supercritically from the linear neutral point s .

The stability of weakly three-dimensional buoyancy-driven boundary layers to travelling waves is considered. It is shown that in the absence of cross ow inviscid modes are unstable and, as the degree of cross ow is increased, the short waves are the ÿrst to be stabilised -longer waves require an enhanced level of three-dimensionality of the basic ow for stabilisation. A combination of asymptotic and numerical techniques are used to provide a complete description of the inviscid modes over the whole wavenumber spectrum. The study is also extended to consider pure vortex "roll-cell" modes which can exist within unstably stratiÿed (buoyancy driven) ows and these are found to stabilise in the presence of cross ow.

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