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The granular monoclinal wave

Published online by Cambridge University Press:  28 March 2018

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 Systems, University of Patras, 26500 Patras, Greece
Giorgos Kanellopoulos
Affiliation:
Department of Mathematics and Center for Research and Applications of Nonlinear Systems, University of Patras, 26500 Patras, Greece Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Ko van der Weele*
Affiliation:
Department of Mathematics and Center for Research and Applications of Nonlinear Systems, University of Patras, 26500 Patras, Greece
*
†Email address for correspondence: [email protected]
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Abstract

We study granular chute flow using the classic Saint-Venant approach, with the shear stresses within the granular sheet being incorporated via a friction law due to Pouliquen & Forterre (J. Fluid Mech., vol. 453, 2002, pp. 113–151) and with the in-plane stresses (which are ignored in the traditional formulation for normal fluids) being represented by a viscous-like term recently derived by Gray & Edwards (J. Fluid Mech., vol. 755, 2014, pp. 503–534). On the basis of this model, we predict that the granular sheet is able to sustain monoclinal waves, i.e. travelling shock structures that monotonically connect a thick region of uniform flow to a thinner one. We examine the balance of forces that determine the shape of this particular waveform and give the precise window of system parameters for which monoclinal waves are expected to appear in experiments.

JFM classification

Granular media: Granular media Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 843 , 25 May 2018 , pp. 810 - 846
Copyright
© 2018 Cambridge University Press 

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