Journal of Fluid Mechanics

Papers

Granular column collapses down rough, inclined channels

GERT LUBEa1, HERBERT E. HUPPERTa2 c1, R. STEPHEN J. SPARKSa3 and ARMIN FREUNDTa4

a1 Volcanic Risk Solutions, Massey University, Palmerston North, Private Bag 11222, New Zealand

a2 Department of Applied Mathematics and Theoretical Physics, Institute of Theoretical Geophysics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

a3 Department of Earth Sciences, Centre of Environmental and Geophysical Flows, Bristol University, Bristol BS8 1RJ, UK

a4 Research Division ‘Dynamics of the Ocean Floor,’ IFM-GEOMAR, Leibniz Institute for Marine Sciences, Wischhofstrasse 1-3, D-24148 Kiel, Germany

Abstract

We present experimental results for the collapse of rectangular columns of sand down rough, inclined, parallel-walled channels. Results for basal inclination θ varying between 4.2° and 25° are compared with previous results for horizontal channels. Shallow-water theory can be usefully combined with scaling relationships obtained by dimensional analysis to yield analytical functions of the maximum runout distance, the maximum deposit height and the time to reach the maximum runout. While the theory excellently predicts the maximum lengths of the deposit it generally overestimates the runout time. The inertial flows are characterized by a moving internal interface separating upper flowing and lower static regions of material. In an initial free-fall phase of collapse the deposited area (= volume per unit width) below the internal interface varies with the square-root of time, independent of the initial height of the column and channel inclination. In the subsequent, lateral spreading phase the deposition rate decreases with increasing basal inclination or with decreasing initial height. The local deposition rate at any fixed distance is a constant, dependent on the column aspect ratio, the channel inclination and the longitudinal position, but invariant with flow velocity and depth. In the lateral spreading phase, vertical velocity profile in the flowing layer take a universal form and are independent of flow depth and velocity. They can be characterized by a shear rate as a function of channel inclination and a length scale describing the fraction of the column involved in flow.

(Received August 12 2008)

(Revised December 23 2010)

(Accepted January 06 2011)

(Online publication April 04 2011)

Key words:

  • granular media

Correspondence:

c1 Email address for correspondence: heh1@esc.cam.ac.uk

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