Rees, DAS and Bassom, AP, The nonlinear non-parallel wave instability of boundary-layer flow induced by a horizontal heated surface in porous media, Journal of Fluid Mechanics, 253 pp. 267-295. ISSN 0022-1120 (1993) [Refereed Article]
Copyright 1993 Cambridge University Press
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.
|Item Type:||Refereed Article|
|Research Division:||Mathematical Sciences|
|Research Group:||Applied mathematics|
|Research Field:||Theoretical and applied mechanics|
|Objective Division:||Expanding Knowledge|
|Objective Group:||Expanding knowledge|
|Objective Field:||Expanding knowledge in the mathematical sciences|
|UTAS Author:||Bassom, AP (Professor Andrew Bassom)|
|Web of Science® Times Cited:||21|
|Deposited By:||Mathematics and Physics|
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