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A dynamical systems view of granular flow: from monoclinal flood waves to roll waves

Published online by Cambridge University Press:  23 April 2019

Dimitrios Razis ,
Giorgos Kanellopoulos  and
Ko van der Weele Open the ORCID record for Ko van der Weele [Opens in a new window]
Dimitrios Razis
Affiliation:
Department of Mathematics and Center for Research and Applications of Nonlinear Science, University of Patras, 26500 Patras, Greece
Giorgos Kanellopoulos
Affiliation:
Department of Mathematics and Center for Research and Applications of Nonlinear Science, University of Patras, 26500 Patras, Greece
Ko van der Weele*
Affiliation:
Department of Mathematics and Center for Research and Applications of Nonlinear Science, University of Patras, 26500 Patras, Greece
*
†Email address for correspondence: weele@math.upatras.gr
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Abstract

On the basis of the Saint-Venant equations for flowing granular matter, we study the various travelling waveforms that are encountered in chute flow for growing Froude number. Generally, for $Fr<2/3$ one finds either a uniform flow of constant thickness or a monoclinal flood wave, i.e. a shock structure monotonically connecting a thick region upstream to a shallower region downstream. For $Fr>2/3$ both the uniform flow and the monoclinal wave cease to be stable; the flow now organizes itself in the form of a train of roll waves. From the governing Saint-Venant equations we derive a dynamical system that elucidates the transition from monoclinal waves to roll waves. It is found that this transition involves several intermediate stages, including an undular bore that had hitherto not been reported for granular flows.

JFM classification

Waves/Free-surface Flows: Channel flow Granular media: Granular media Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , pp. 143 - 181
Copyright
© 2019 Cambridge University Press 

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