ANZIAM  J.  46 (2005), 507-543
The stability of a curved, heated boundary layer: linear and nonlinear problems

C. E. Watson
  Quintessa Limited
  Dalton House
  Newtown Road
  Oxfordshire RG9 1HG
S. R. Otto
  R&A Rules Limited
  Beach House
  Golf Place
  St Andrews KY16 9JA

We consider the stability of high Reynolds number flow past a heated, curved wall. The influence of both buoyancy and curvature, with the appropriate sense, can render a flow unstable to longitudinal vortices. However, conversely each mechanism can make a flow more stable; as with a stable stratification or a convex curvature. This is partially due to their influence on the basic flow and also due to additional terms in the stability equations. In fact the presence of buoyancy in combination with an appropriate local wall gradient can actually increase the wall shear and these effects can lead to supervelocities and the promotion of a wall jet. This leads to the interesting discovery that the flow can be unstable for both concave and convex curvatures. Furthermore, it is possible to observe sustained vortex growth in stably stratified boundary layers over convexly curved walls. The evolution of the modes is considered in both the linear and nonlinear régimes.
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