Journal of Fluid Mechanics



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Axisymmetric collapses of granular columns


GERT LUBE a1, HERBERT E. HUPPERT a2, R. STEPHEN J. SPARKS a1 and MARK A. HALLWORTH a2
a1 Centre of Environmental and Geophysical Flows, Department of Earth Sciences, Bristol University, Bristol BS8 1RJ, UK
a2 Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

Article author query
lube g   [Google Scholar] 
huppert h   [Google Scholar] 
sparks r   [Google Scholar] 
hallworth m   [Google Scholar] 
 

Abstract

Experimental observations of the collapse of initially vertical columns of small grains are presented. The experiments were performed mainly with dry grains of salt or sand, with some additional experiments using couscous, sugar or rice. Some of the experimental flows were analysed using high-speed video. There are three different flow regimes, dependent on the value of the aspect ratio $a\,{=}\,h_i/r_i$, where $h_i$ and $r_i$ are the initial height and radius of the granular column respectively. The differing forms of flow behaviour are described for each regime. In all cases a central, conically sided region of angle approximately $ 59^\circ$, corresponding to an aspect ratio of 1.7, remains undisturbed throughout the motion. The main experimental results for the final extent of the deposit and the time for emplacement are systematically collapsed in a quantitative way independent of any friction coefficients. Along with the kinematic data for the rate of spread of the front of the collapsing column, this is interpreted as indicating that frictional effects between individual grains in the bulk of the moving flow only play a role in the last instant of the flow, as it comes to an abrupt halt. For $a\,{<}\,1.7$, the measured final runout radius, $r_\infty$, is related to the initial radius by $r_\infty \,{=}\, r_i(1\,{+}\,1.24a)$; while for $1.7\,{<}\,a$ the corresponding relationship is $r_\infty \,{=}\,r_i(1\,{+}\,1.6a^{1/2})$. The time, $t_\infty$, taken for the grains to reach $r_\infty$ is given by $t_\infty \,{=}\,3(h_i/g)^{1/2}\,{=}\,3(r_i/g)^{1/2}a^{1/2}$, where $g$ is the gravitational acceleration. The insights and conclusions gained from these experiments can be applied to a wide range of industrial and natural flows of concentrated particles. For example, the observation of the rapid deposition of the grains can help explain details of the emplacement of pyroclastic flows resulting from the explosive eruption of volcanoes.

(Received July 30 2003)
(Revised February 5 2004)



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