Front Solutions of Richards’ Equation
- First Online:
Front solutions of the one-dimensional Richards’ equation used to describe groundwater flow are studied systematically for the three soil retention models known as Brooks–Corey, Mualem–Van Genuchten and Storm–Fujita. Both the infiltration problem when water percolates from the surface into the ground under the influence of gravity and the imbibition (absorption) problem when groundwater diffuses in the horizontal direction without the gravity effect are considered. In general, self-similar solutions of the first kind in the form of front exist only for the imbibition case; such solutions are stable against small perturbations. In the particular case of the Brooks–Corey model, self-similar solutions of the second kind in the form of a decaying pulse also exist both for the imbibition and infiltration cases. Steady-state solutions in the form of travelling fronts exist for the infiltration case only. The existence of such solutions does not depend on the specifics of the soil retention model. It is shown numerically that these solutions are stable against small perturbations.
KeywordsConvection–diffusion equation Burgers equation Front solutions Soil physics Infiltration Imbibition Porous media Groundwater flow Richards’ equation Self-similar solution Steady-state solution Water front stability
Unable to display preview. Download preview PDF.
- Barenblatt G.I. (1996) Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge University Press, 386 pGoogle Scholar
- Buckingham, E.: Studies on the movement of soil moisture. U.S. Dept. of Agriculture Bureau of Soils Bull. 38 (1907)Google Scholar
- Philip J.R. (1969). Theory of infiltration. In: Chow, V.T. (eds) Advances in Hydroscience, vol. 5, pp 215–296. Academic Press, NY Google Scholar
- Polubarinova-Kochina, P.Ya.: Theory of Graundwater Movements, 2nd edn. Nauka, Moscow, 664 p (1977) (in Russian). Engl. transl. from the 1st edn.: Princeton University Press, Princeton (1972)Google Scholar
- Scott, A.C. (ed.): Encyclopedia of Nonlinear Science. Routledge, New York and London, 1053 p (2005)Google Scholar
- Smith R.E., Smettem R.J., Broadbridge P. and Woolhiser D.A. (2002). Infiltration Theory for Hydrologic Applications. AGU, Washington, p 212 Google Scholar
- The Mathworks, Inc. http://www.mathworks.com
- Whitham G.B.: Linear and Nonlinear Waves. J. Wiley & Sons, 636 p (1974)Google Scholar