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The nonlinear non-parallel wave instability of boundary-layer flow induced by a horizontal heated surface in porous media

Published online by Cambridge University Press:  26 April 2006

D. A. S. Rees  and
Andrew P. Bassom
D. A. S. Rees
Affiliation:
School of Mechanical Engineering, University of Bath, Claverton Down, Bath, BA2 7AY, UK
Andrew P. Bassom
Affiliation:
Department of Mathematics, University of Exeter, North Park Road, Exeter, Devon, EX4 4QE, UK
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Abstract

The two-dimensional wave instability of convection induced by a semi-infinite heated surface embedded in a fluid-saturated porous medium is studied. Owing to the inadequacy of parallel-flow theories and the inaccuracy of the leading-order boundary-layer approximation at the point of incipient instability given by these theories, the problem has been re-examined using numerical simulations of the full time-dependent nonlinear equations of motion. Small-amplitude localized disturbances placed in the steady boundary layer are shown to propagate upstream much faster than they advect downstream. There seems to be a preferred wavelength for the evolving disturbance while it is in the linear regime, but the local growth rate depends on the distance downstream and there is a smooth, rather than an abrupt, spatial transition to convection.

The starting problem, where the temperature of the horizontal surface is instantaneously raised from the ambient, is found to give rise to a particularly violent fluid motion near the leading edge. A strong thermal plume is generated which is eventually advected downstream. The long-term evolution of the instability is computed. The flow does not settle down to a steady or a time-periodic state, and evidence is presented which suggests that it is inherently chaotic. The evolving flow field exhibits a wide range of dynamical behaviour including cell merging, the ejection of hot fluid from the boundary layer, and short periods of relatively intense fluid motion accompanied by boundary-layer thinning and short-wavelength waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 253 , August 1993 , pp. 267 - 295
Copyright
© 1993 Cambridge University Press

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