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Draining viscous gravity currents in a vertical fracture

Published online by Cambridge University Press:  17 June 2002

DAVID PRITCHARD
Affiliation:
Centre for Environmental and Geophysical Flows, School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
ANDREW J. HOGG
Affiliation:
Centre for Environmental and Geophysical Flows, School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK

Abstract

We consider the flow of instantaneous releases of a finite volume of viscous fluid in a narrow vertical fracture or Hele-Shaw cell, when there is a still narrower vertical crack in the horizontal base of the cell. The predominant motion is over the horizontal surface, but fluid also drains through the crack, progressively diminishing the volume of the current in the fracture. When the crack is shallow on the scale of the current, it saturates immediately with the draining fluid. In this case, we obtain an exact analytical solution for the motion. When the crack is deeper and does not saturate immediately, we calculate numerically the motion of the fluid in both the fracture and the crack. In each case the current advances to a finite run-out length and then retreats: we describe both phases of the motion and characterize the run-out length in terms of the controlling parameters.

Type
Research Article
Copyright
© 2002 Cambridge University Press

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