Spreading of a Gravity Current over a Permeable Surface
Publication: Journal of Hydraulic Engineering
Volume 128, Issue 5
Abstract
Plane inertial gravity currents running over horizontal permeable surfaces are studied. An analytical simple model based on local and global balances is derived which describes the propagation and infiltration of an incompressible dense fluid on and through the surface. Results of laboratory experiments are presented which are in accordance with scaling laws suggested analytically. It is found that the loss of mass, the velocity, and the position of the front of the current follow exponential relationships. The dynamics is governed by a particular decay time related to the initial volume released and reduced gravity However this decay time exhibits a different functional relationship from that obtained for currents evolving over thin permeable bottoms when the downward flow is viscous. As a consequence of the loss of mass, the distance to extinction of the current is found to be independent of
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References
Batchelor, G. K. (1967). An introduction to fluid dynamics, Cambridge University Press.
Bear, J. (1972). Dynamics of fluids in porous media, Elsevier, New York.
Britter, R. E.(1989). “Atmospheric dispersion of dense gases.” Annu. Rev. Fluid Mech., 21, 317–344.
Dalziel, S. B.(1993). “Rayleigh-Taylor instability: experiments with image analysis.” Dyn. Atmos. Oceans, 20, 127–153.
Dalziel, S. B. (1995). DigImage: System Overview, Cambridge Environmental Research Consultants.
Duillen, F. A. L. (1979). Porous media. Fluid transport and pore structure, Academic, New York.
Dussan, V.and Auzerais, E. B.(1993). “Buoyancy-induced flow in porous media generated near a drilled oil well. Part 1. The accumulation of filtrate at a horizontal impermeable boundary.” J. Fluid Mech., 254, 283–311.
Fannelop, T. K., and Waldman, G. D.(1972). “Dynamics of oil slicks.” AIAA J., 10, 506–510.
Gratton, J., and Vigo, C.(1994). “Self-similar gravity currents with variable inflow revisited: plane currents.” J. Fluid Mech., 258, 77–104.
Grundy, R. E., and Rottman, J. W.(1985). “The approach to self-similarity of the solutions of the shallow-water equations representing gravity-current releases.” J. Fluid Mech., 156, 39–53.
Huppert, H. E., and Simpson, J. E.(1980). “The slumping of the gravity currents.” J. Fluid Mech., 99, 785–799.
Landau, L. D., and Lifshitz, E. M. (1987). Course of theoretical physics, Vol. 6: Fluid mechanics, 2nd Ed., Pergamon, New York.
Lionet, J., and Quoy, O. (1995). “Gravity currents over porous media.” Internal Rep., DAMTP, Univ. of Cambridge.
Moodie, T. B., and Pascal, J. P.(1999a). “Downslope movement of compositionally driven gravity flows over porous surfaces.” J. Porous Media, 2(2), 127–141.
Moodie, T. B., and Pascal, J. P.(1999b). “Axisymmetric spreading and filtration of inclined thermals over porous surfaces.” Can. Appl. Math. Q., 7(2), 185–201.
Rottman, J. W., and Simpson, J. E.(1983). “Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel.” J. Fluid Mech., 135, 95–110.
Simpson, J. E. (1997). Gravity currents in the environment and the laboratory, Cambridge University Press, U.K.
Thomas, L. P., Marino, B. M., and Linden, P. F.(1998). “Gravity currents over porous substrates.” J. Fluid Mech., 366, 239–258.
Ungarish, M., and Huppert, H. E.(2000). “Gravity currents over a porous boundary: shallow-water solutions and box-model approximations.” J. Fluid Mech., 418, 1–23.
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Information
Published In
Journal of Hydraulic Engineering
Volume 128 • Issue 5 • May 2002
Pages: 527 - 533
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Jul 17, 2000
Accepted: Oct 25, 2001
Published online: Apr 15, 2002
Published in print: May 2002
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