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On ice-induced instability in free-surface flows

Published online by Cambridge University Press:  19 April 2007

Department of Aerospace Sciences, Cranfield University, Cranfield MK43 0AL, UK
Department of Mathematics, University College London, Gower Street, London WC1 6BT, UK


The problem of stability of a water-coated ice layer is investigated for a free-surface flow of a thin water film down an inclined plane. An asymptotic (double-deck) theory is developed for a flow with large Reynolds and Froude numbers which is then used to investigate linear two-dimensional, three-dimensional and nonlinear two-dimensional stability characteristics. A new mode of upstream-propagating instability arising from the interaction of the ice surface with the flow is discovered and its properties are investigated. In the linear limit, closed-form expressions for the dispersion relation and neutral curves are obtained for the case of Pr = 1. For the general case, the linear stability problem is solved numerically and the applicability of the solution with Pr = 1 is analysed. Nonlinear double-deck equations are solved with a novel global-marching-type scheme and the effects of nonlinearity are investigated. An explanation of the physical mechanism leading to the upstream propagation of instability waves is provided.

Copyright © Cambridge University Press 2007

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