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Granular and fluid washboards

Published online by Cambridge University Press:  05 January 2012

I. J. Hewitt ,
N. J. Balmforth  and
J. N. McElwaine
I. J. Hewitt*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
N. J. Balmforth
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
J. N. McElwaine
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the dynamics of an object towed over the surface of an initially flat, deformable layer. Using a combination of simple laboratory experiments and a theoretical model, we demonstrate that an inclined plate, pivoted so as to move up and down, may be towed steadily over a substrate at low speed, but become unstable to vertical oscillations above a threshold speed. That threshold depends upon the weight of the plate and the physical properties of the substrate, but arises whether the substrate is a viscous fluid, a viscoplastic fluid, or a granular medium. For the latter two materials, the unstable oscillations imprint a permanent rippled pattern on the layer, suggesting that the phenomenon of the ‘washboard road’ can arise from the passage of a single vehicle (i.e. the absolute instability of a flat bed). We argue that the mechanism behind the instability originates from the mound of material that is pushed forward ahead of the object: the extent of the mound determines the resultant force, whereas its growth is controlled by the object’s height relative to the undisturbed surface, allowing for an unstable coupling between the vertical motion and the substrate deformation.

JFM classification

Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 692 , 10 February 2012 , pp. 446 - 463
Copyright
Copyright © Cambridge University Press 2012

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