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.

    ORCID iDs

    Pritchard, David ORCID logoORCID: https://orcid.org/0000-0002-9235-7052, Duffy, Brian R. ORCID logoORCID: https://orcid.org/0000-0003-2687-7938 and Wilson, Stephen K. ORCID logoORCID: https://orcid.org/0000-0001-7841-9643;
    • Item type:Article
      ID code:48744
      Dates:
      Date
      Event
      October 2015
      Published
      1 November 2014
      Published Online
      2 July 2014
      Accepted
      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:11 Sep 2021 02:15
      Related URLs:
      URI:https://strathprints.strath.ac.uk/id/eprint/48744
    CORE (COnnecting REpositories)