HR: 1340h
AN: H33B-0469    [Abstracts]
TI: Modeling Conditional Stability of Gravity-Driven Unsaturated Infiltrating Flows Using a Non-equilibrium Capillary Pressure-Saturation Relation
AU: Dautov, R Z
EM: Rafail.Dautov@ksu.ru
AF: Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, 17 Universitetskaya Street, Kazan, 420008 Russian Federation
AU: Egorov, A G
EM: Andrey.Egorov@ksu.ru
AF: Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, 17 Universitetskaya Street, Kazan, 420008 Russian Federation
AU: * Nieber, J L
EM: nieber@umn.edu
AF: Department of Biosystems and Agricultural Engineering, University of Minnesota, 1390 Eckles Ave, St. Paul, MN 55108 United States
AU: Sheshukov, A Y
EM: shesh002@umn.edu
AF: Department of Biosystems and Agricultural Engineering, University of Minnesota, 1390 Eckles Ave, St. Paul, MN 55108 United States
AB: Gravity-driven unstable flow during infiltration in unsaturated porous media is considered to be an important preferential flow process. The conventional equation for modeling unsaturated flows is the Richards equation, but this equation cannot be used to model unstable flows as it has been shown (A.G. Egorov, R.Z. Dautov, J.L. Nieber, and A.Y. Sheshukov, 2003. Stability analysis of gravity-assisted infiltrating flow, Water Resour. Res., 39:,1266, doi:10.1029/2002WR001886) that solutions to the Richards equations are unconditionally stable. Therefore, modeling these unstable flows requires the use of new forms of the mass balance equation which contain features that might account for the cause of instabilities. One postulated cause for instabilities is the existence of non-equilibrium in the capillary pressure-saturation relation. In this presentation we will examine the conditional stability that results from the use of a non-equilibrium relation of the form $\tau(S,p){\partial S}/{\partial t}=p-P(S)$, where $\tau$ is the relaxation coefficient, $S$ is the saturation, $p$ is the dynamic pressure, and $P(S)$ is the equilibrium pressure. The stability analysis is based on the perturbation of the traveling wave form of the governing mass balance equation and the associated relaxation equation. The numerical determination of the eigenvalues of the resulting perturbation equations yields the critical growth factor as related to perturbation frequency. The derived critical growth factor is used in evaluating the conditional stability as to its sensitivity to the flux and magnitude of the relaxation coefficient. It is interesting to see that as $\tau(S,p)\rightarrow 0$ the flow becomes unconditionally stable, the result being that found for the Richards equation. The perturbation frequency associated with the critical growth factor is related to finger width and this is confirmed with simulations in the two-dimensional vertical plane.
DE: 1866 Soil moisture
DE: 1875 Unsaturated zone
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting