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Title:Stability of viscous stratified free surface flow at low reynolds number with reference to modelling of rock glaciers
Author(s):Loewenherz, Deborah S.; Lawrence, Christopher J.
Subject(s):Low Reynolds Number Flow
Rock Glacier Forms
Viscous Stratified Free Surface Flows
Abstract:The stability of low Reynolds number flow on an inclined plane is investigated with respect to modelling the initiation of transverse wave-like ridges which commonly occur on the surface of rock glacier forms and appear to result from an instability in the physical system. A linear analysis is used to assess the effects which viscosity stratification has on flow stability. Results indicate that when the viscosity of an upper layer of fluid is greater than that of the lower layer, the system is unstable. This instability is manifested in waves having finite wavelength rather than the long waves which are implied by previous research. The response of the free surface profile to a discontinuity in the slope of the incline is also considered, both for the flow of a single fluid layer and for a system consisting of two layers of differing viscosity, and is found to resemble a smoothed step function in character, as expected. It is concluded that surficial ridges develop as a result of a slope discontinuity which serves to amplify incipient instability present in the system. The effects of a thin elastic upper lamina on the stability of a single layer of fluid are also examined. The results suggest, alternatively, that surface ridges represent buckling which occurs in response to a critical compressive load in the lamina induced by a change in the slope of the incline.
Issue Date:1988-08
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 488
Genre:Technical Report
Rights Information:Copyright 1988 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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