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The Quarterly Journal of Mechanics and Applied Mathematics 2000 53(3):475-495; doi:10.1093/qjmam/53.3.475
© 2000 by Oxford University Press
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Nonlinear convection in the boundary layer above a sinusoidally heated flat plate

ANDREW MAY1,+ and ANDREW P. BASSOM2,§

( 1 Tessella Support Services plc, 3Vineyard Chambers, Abingdon, Oxon OX14 3PX 2 School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia )

The thermal boundary layer induced within a horizontal semi-infinite layer of Boussinesq fluid by a sinusoidally heated bounding plate is known to be susceptible to vortex instability. The structure of short wavelength convection is considered here and the analysis taken from linear, through weakly nonlinear and onto the fully nonlinear stage. At this point the activity is sufficiently strong that it induces large changes in the underlying thermal profile and the overall flow characteristics are determined by the solution of a free boundary-value problem. This solution demonstrates that the highly nonlinear vortices tend to settle into a periodic form in which intervals of intense activity alternate with times of relative quiescence.

Received 19 March, 1999. Revised 28 January, 2000.

+ <Andrew.May@tessella.co.uk>

§ Present address: School of Mathematical Sciences, North Park Road, University of Exeter, Exeter, Devon EX4 4QE. <drew@maths.exeter.ac.uk>


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