HR: 16:20h
AN: H22J-02    [PDF]
TI: Dynamic Capillary Pressure Mechanism for Instability in Gravity-Driven Unsaturated Flows
AU: * Nieber, J L
EM: nieber@umn.edu
AF: University of Minnesota, Department of Biosystems and Agricultural Engineering 1390 Eckles Ave., St. Paul, MN 55108 United States
AU: Dautov, R Z
EM: rdautov@ksu.ru
AF: Kazan State University, Department of Computational Mathematics and Cybernetics 18 Kremlevskaya Street, Kazan, 420008 Russian Federation
AU: Egorov, A G
EM: andrey.egorov@ksu.ru
AF: Kazan State University, Chebotarev Research Institute of Mathematics and Mechanics, 17 Universitetskaya Street, Kazan, 420008 Russian Federation
AU: Sheshukov, A Y
EM: shesh002@umn.edu
AF: University of Minnesota, Department of Biosystems and Agricultural Engineering 1390 Eckles Ave., St. Paul, MN 55108 United States
AB: Several alternative models for describing water flow in unsaturated porous media are presented. These models are each based on an equation for conservation of mass of water, and a generalized linear law for water flux (Darcy's law) containing a term referred to as the dynamic capillary pressure. The distinct form of each alternative model is based on the specific form of expression used to describe the dynamic capillary pressure. The conventional model arises when this pressure is set equal to the equilibrium pressure given by the capillary pressure - saturation function for unsaturated porous media, and this formulation leads to the Richards Equation(RE). Other models are derived by representing the dynamic capillary pressure by a rheological relationship stating that the dynamic capillary pressure is not given directly by the capillary pressure - saturation function. Two forms of rheological relationship are considered in this manuscript, a general non-equilibrium relation, and a more specific relation expressed by a first-order kinetic equation referred to as a relaxation relation. For the general non-equilibrium relation the model equation system is called the general Non-Equilibrium Richards Equation(NERE) model, and for the case of the relaxation relation the model system is called the Relaxation Non-Equilibrium Richards Equation(RNERE) model. Each of the alternative models is analyzed for flow characteristics under gravity-dominant conditions by using a traveling wave transformation of the equations for each model, and more importantly the flow described by each model is analyzed for linear stability. It is shown that when a flow field is perturbed by infinitesimal disturbances, the RE is unconditionally stable, while both the NERE and the RNERE are conditionally stable. Instability of flows for the NERE and the RNERE models are shown to be related to the saturation and pressure profiles being sufficienlty non-monotonic. Through a nonlinear stability analysis it is shown that flows for the RE are unconditionally stable not only to infinitesimal disturbances but to finite disturbances as well for both homogeneous and heterogeneous porous media.
DE: 1866 Soil moisture
DE: 1875 Unsaturated zone
DE: 3210 Modeling
SC: Hydrology [H]
MN: 2003 Fall Meeting