Shallow flows of generalised Newtonian fluids on an inclined plane
Pritchard, David and Duffy, Brian R. and Wilson, Stephen K. (2015) Shallow flows of generalised Newtonian fluids on an inclined plane. Journal of Engineering Mathematics, 94 (1). pp. 115-133. ISSN 0022-0833
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Abstract
We derive a general evolution equation for a shallow layer of a generalised Newtonian fluid undergoing two-dimensional gravity-driven flow on an inclined plane. The flux term appearing in this equation is expressed in terms of an integral involving the prescribed constitutive relation and, crucially, does not require explicit knowledge of the velocity profile of the flow; this allows the equation to be formulated for any generalised Newtonian fluid. In particular, we develop general solutions for travelling waves on a mild slope and for kinematic waves on a moderately steep slope; these results provide simple and accessible models of, for example, the propagation of non-Newtonian mud and debris flows.
Creators(s): |
Pritchard, David ![]() ![]() ![]() | Item type: | Article |
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ID code: | 48744 |
Keywords: | non-Newtonian rheology, lubrication flow, free-surface flow, thin film, Mathematics, Mathematics(all) |
Subjects: | Science > Mathematics |
Department: | Faculty of Science > Mathematics and Statistics |
Depositing user: | Pure Administrator |
Date deposited: | 23 Jun 2014 15:48 |
Last modified: | 25 Jan 2021 03:17 |
Related URLs: | |
URI: | https://strathprints.strath.ac.uk/id/eprint/48744 |
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