Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane

Rajagopal, K.R., Saccomandi, G. and Vergori, L. (2012) Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane. Journal of Fluid Mechanics, 706, pp. 173-189. (doi: 10.1017/jfm.2012.244)

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Publisher's URL: http://dx.doi.org/10.1017/jfm.2012.244


In this paper we consider a fluid whose viscosity depends on both the mean normal stress and the shear rate flowing down an inclined plane. Such flows have relevance to geophysical flows. In order to make the problem amenable to analysis, we consider a generalization of the lubrication approximation for the flows of such fluids based on the development of the generalization of the Reynolds equation for such flows. This allows us to obtain analytical solutions to the problem of propagation of waves in a fluid flowing down an inclined plane. We find that the dependence of the viscosity on the pressure can increase the breaking time by an order of magnitude or more than that for the classical Newtonian fluid. In the viscous regime, we find both upslope and downslope travelling wave solutions, and these solutions are quantitatively and qualitatively different from the classical Newtonian solutions.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Vergori, Dr Luigi
Authors: Rajagopal, K.R., Saccomandi, G., and Vergori, L.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Fluid Mechanics
Journal Abbr.:J. Fluid Mech.
Publisher:Cambridge University Press
ISSN (Online):1469-7645
Copyright Holders:Copyright © 2012 Cambridge University Press
First Published:First published in Journal of Fluid Mechanics 706:173-189
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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