### Abstract

Language | English |
---|---|

Pages | 207-216 |

Number of pages | 10 |

Journal | Journal of Fluid Mechanics |

Volume | 459 |

DOIs | |

Publication status | Published - 2002 |

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### Keywords

- fluid mechanics
- mathematical analysis
- viscous gravity currents i

### Cite this

*Journal of Fluid Mechanics*,

*459*, 207-216. https://doi.org/10.1017/S0022112002008327

}

*Journal of Fluid Mechanics*, vol. 459, pp. 207-216. https://doi.org/10.1017/S0022112002008327

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Draining viscous gravity currents in a vertical fracture

AU - Pritchard, David

AU - Hogg, Andrew J.

PY - 2002

Y1 - 2002

N2 - 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.

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

U2 - 10.1017/S0022112002008327

DO - 10.1017/S0022112002008327

M3 - Article

VL - 459

SP - 207

EP - 216

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -