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The stability of a curved, heated boundary layer: linear and nonlinear problems

Published online by Cambridge University Press:  17 February 2009

C. E. Watson  and
S. R. Otto
C. E. Watson
Affiliation:
Quintessa Limited, Dalton House, Newtown Road, Henley-On-Thames, Oxfordshire, RG9 IHG, England.
S. R. Otto
Affiliation:
R&A Rules Limited, Beach House, Golf Place, St Andrews, KY16 9JA, Scotland; e-mail: [email protected].
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 4 , April 2005 , pp. 507 - 543
Copyright
Copyright © Australian Mathematical Society 2005

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