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On ice-induced instability in free-surface flows

Published online by Cambridge University Press:  19 April 2007

EVGENIY SHAPIRO  and
SERGEI TIMOSHIN
EVGENIY SHAPIRO
Affiliation:
Department of Aerospace Sciences, Cranfield University, Cranfield MK43 0AL, UK
SERGEI TIMOSHIN
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1 6BT, UK
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Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 577 , 25 April 2007 , pp. 25 - 52
Copyright
Copyright © Cambridge University Press 2007

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