Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#244234] of Thomas P. Witelski

search www.ams.org.

Papers Published

  1. DiCarlo, DA; Juanes, R; LaForce, T; Witelski, TP, Nonmonotonic traveling wave solutions of infiltration into porous media, Water Resources Research, vol. 44 no. 2 (February, 2008), pp. W02406, ISSN 0043-1397 [2007WR005975], [doi]
    (last updated on 2017/12/15)

    Abstract:
    In uniform soils that are susceptible to unstable preferential flow, the water saturation may exhibit a nonmonotonic profile upon continuous infiltration. As this nonmonotonicity (also known as saturation overshoot) cannot be described by the conventional Richards equation, there have been proposed possible extensions to the unsaturated flow equations, including a nonmonotonic capillary pressure-saturation curve and a second-order hyperbolic term. Here, we present analytic traveling wave solutions to the extended Richards equation. These new solutions indeed display a nonmonotonic saturation profile, similar to previous simulation results. We show that these extensions need a regularization term to produce a unique solution. We develop complete analytic solutions using a relaxation regularization term, and we discuss the results in terms of recent measurements of saturation overshoot. Copyright 2008 by the American Geophysical Union.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320