ANZIAM J.
43 (2002), 333358

The stability of boundary layers on curved heated plates

Jillian A. K. Stott
Department of Applied Mathematics
The University of Adelaide
Adelaide SA 5005
Australia


and

James P. Denier
Department of Applied Mathematics
The University of Adelaide
Adelaide SA 5005
Australia



Abstract

We consider the effect the competing mechanisms
of buoyancydriven acceleration (arising from
heating a surface) and streamline curvature (due
to curvature of a surface) have on the stability
of boundarylayer flows. We confine our
attention to vortex type instabilities (commonly
referred to as Gortler 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 boundarylayer flow over
a heated (or cooled) curved rigid body. In the
absence of buoyancy forcing the flow is
centrifugally unstable to counterrotating
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 (freestream) 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 unstable flow stable.

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