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
Abstract
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 |
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Status: | Published |
Refereed: | Yes |
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: | 0022-1120 |
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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