Inertial Density Currents over Porous Media Limited by Different Lower Boundary Conditions
Publication: Journal of Hydraulic Engineering
Volume 138, Issue 2
Abstract
We study the evolution of two-dimensional high-Reynolds-number density currents propagating over horizontal porous substrates initially saturated with a lighter fluid when an impermeable surface under the bed is used and a Darcy flow through the medium takes place. Laboratory experiments were performed varying the initial characteristic parameters such as the volume released, the height-to-width ratio of the dense fluid, the relative density difference between the current and ambient fluids, and the bed depth. The dynamic changes of the gravity-driven flow and the influence of the thickness of the porous substrate are described by means of an empirical analysis that considers two lower boundary conditions of the bed, that is, when it is bounded from below by an impermeable or a permeable layer. Thus, the new experimental results are integrated to previous findings in a unified theoretical treatment. In the present case, the dense fluid penetrates into the porous layer pushing the lighter one through the upper boundary located ahead of the current, as shown by the vorticity distribution, and modifying the interaction between the flows over and inside the bed. This flow in the neighborhood of the front, although important, is smaller than the one that would pass through the lower boundary if this were permeable.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial support for this study was provided by ANPCyT (UNSPECIFIEDPICT 1185/06) and CONICET (UNSPECIFIEDPIP 0054/10), Argentina.
References
Acton, J. M., Huppert, H. E., and Worster, M. G. (2001). “Two-dimensional viscous gravity currents flowing over a deep porous medium.” J. Fluid Mech., 440, 359–380.
Bear, J. (1972). Dynamics of fluids in porous media, Elsevier, New York.
Dalziel, S. B. (2006). DigiFlow User Guide, 〈http://www.dalzielresearch.com/digiflow/〉 (Jan. 20, 2012).
Gratton, J., and Vigo, C. (1994). “Self-similar gravity currents with variable inflow revisited: Plane currents.” J. Fluid Mech., 258, 77–104.
Gratton, R., Diez, J. A., Thomas, L. P., Marino, B. M., and Betelu, S. (1996). “Quasi-self-similarity for wetting drops.” Phys. Rev. E, 53(4), 3563–3572.
Haber, S., and Mauri, R. (1983). “Boundary conditions for Darcy’s flow through porous media.” Int J. Multiphas Flow, 9(5), 561–574.
Hacker, J., Linden, P. F., and Dalziel, S. B. (1996). “Mixing in lock-release gravity currents.” Dyn. Atmos. Oceans, 24(1–4), 183–195.
Marino, B. M., and Thomas, L. P. (2002). “The spreading of a gravity current over a permeable surface.” J. Hydraul. Eng., 128(5), 527–533.
Marino, B. M., and Thomas, L. P. (2010). “Gravity flows associated with erosive-sedimentary processes in rivers and estuaries beds.” Proc. Latin American Congress on Hydraulics, IAHR, Punta del Este, Uruguay, 1A_335.
Marino, B. M., Thomas, L. P., and Linden, P. F. (2005). “The front condition for gravity currents.” J. Fluid Mech., 536, 49–78.
Moodie, T. B., and Pascal, J. P. (1999a). “Axisymmetric spreading and filtration of inclined thermals over porous surfaces.” Can. Appl. Math. Q., 7(2), 185–201.
Moodie, T. B., and Pascal, J. P. (1999b). “Downslope movement of compositionally driven gravity currents over porous surfaces.” J. Porous Media, 2(2), 127–141.
Prinos, P., Sofialidis, D., and Keramaris, E. (2003). “Turbulent flow over and within a porous bed.” J. Hydraul. Eng., 129(9), 720–733.
Pritchard, D., and Hogg, A. J. (2002). “Draining viscous gravity currents in a vertical fracture.” J. Fluid Mech., 459, 207–216.
Pritchard, D., Woods, A. W., and Hogg, A. J. (2001). “On the slow draining of a gravity current moving through a layered permeable medium.” J. Fluid Mech., 444, 23–47.
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, Cambridge, U.K.
Spannuth, M. J., Neufeld, J. A., Wettlaufer, J. S., and Worster, M. G. (2009). “Axisymmetric viscous gravity currents flowing over a porous medium.” J. Fluid Mech., 622, 135–144.
Thomas, L. P., Dalziel, S. B., and Marino, B. M. (2003). “The structure of the head of an inertial gravity current determined by particle tracking velocimetry.” Exp. Fluids, 34(6), 708–716.
Thomas, L. P., Marino, B. M., and Linden, P. F. (1998). “Gravity currents over porous substrates.” J. Fluid Mech., 366, 239–258.
Thomas, L. P., Marino, B. M., and Linden, P. F. (2004). “Lock-release inertial gravity currents over a thick porous layer.” J. Fluid Mech., 503, 299–319.
Ungarish, M., and Huppert, H. E. (2000). “High-Reynolds number gravity currents over a porous boundary: Shallow-water solutions and box-model approximations.” J. Fluid Mech., 418, 1–23.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 138 • Issue 2 • February 2012
Pages: 133 - 142
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Nov 15, 2010
Accepted: Jun 21, 2011
Published online: Jun 23, 2011
Published in print: Feb 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.