Draining viscous gravity currents in a vertical fracture

David Pritchard, Andrew J. Hogg

Research output: Contribution to journalArticle

16 Citations (Scopus)

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.
LanguageEnglish
Pages207-216
Number of pages10
JournalJournal of Fluid Mechanics
Volume459
DOIs
Publication statusPublished - 2002

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drainage
Gravitation
cracks
gravitation
Cracks
Fluids
fluids
viscous fluids
cells

Keywords

  • fluid mechanics
  • mathematical analysis
  • viscous gravity currents i

Cite this

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Draining viscous gravity currents in a vertical fracture. / Pritchard, David; Hogg, Andrew J.

In: Journal of Fluid Mechanics, Vol. 459, 2002, p. 207-216.

Research output: Contribution to journalArticle

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AU - Pritchard, David

AU - Hogg, Andrew J.

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AB - 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.

KW - fluid mechanics

KW - mathematical analysis

KW - viscous gravity currents i

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