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On the long-wave instability of natural-convection boundary layers

Published online by Cambridge University Press:  25 March 1997

P. G. DANIELS  and
JOHN C. PATTERSON
P. G. DANIELS
Affiliation:
Department of Mathematics, City University, Northampton Square, London EC1V 0HB, UK
JOHN C. PATTERSON
Affiliation:
Centre for Water Research, University of Western Australia, Nedlands W.A. 6009, Australia
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Abstract

This paper considers the stability of the one-dimensional boundary layer generated by sudden heating of an infinite vertical wall. A quasi-steady approximation is used to analyse the asymptotic form of the lower branch of the neutral curve, corresponding to disturbances of wavelength much greater than the boundary-layer width. This leads to predictions of the critical wavenumber for neutral stability and the maximum phase speed of the travelling waves. Results are obtained for a range of Prandtl numbers and are compared with solutions of the full stability equations and with numerical simulations and experimental observations of cavity flows driven by sudden heating of the sidewalls.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 335 , 25 March 1997 , pp. 57 - 73
Copyright
© 1997 Cambridge University Press

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