Snippets from Soil-Water Infiltration: Where Approximate Becomes Exact

Host Institution:

RMIT University

Title of Seminar:

Snippets from Soil-Water Infiltration: Where Approximate Becomes Exact

Speaker's Name:

Prof Phil Broadbridge

Speaker's Institution:

La Tobe University

Time and Date:

Friday 1 June 2012, 3:30pm (AEST)

Seminar Abstract:

Water flow in unsaturated soil is well described by a nonlinear diffusion-convection equation whose transport coefficients increase strongly with water content.  Basic understanding of the dynamics has come mostly  from analysis of the Dirichlet problem with constant-concentration boundary conditions; in the 1950s J.R. Philip showed by symmetry arguments that the early-time cumulative infiltration is proportional to √t, the first term of  a √t power series. Since the 1980s, several research groups have used an integrable one-dimensional version of Richards’ equation,  with realistic  nonlinear transport coefficients, to predict experimentally verifiable quantities.  Neat expressions emerge for time to incipient surface ponding under constant-rainfall (Robin-type) boundary conditions, for the dependence of sorptivity (leading-order infiltration coefficient) on pond depth and for the second and higher infiltration coefficients. These exact results are at odds with those of the traditional Green-Ampt model, whose shortcomings have been exposed after 101 years.

The integrable model under Dirichlet boundary conditions transforms to a perturbed classical Stefan problem  that can be solved by a formal series after separation of variables. This leads to general questions about when such a construction is possible. The best known approaches to separation are the canonical coordinates of a symmetry, and the Staeckel matrix construction.

Seminar Convenors:

This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it.

AGR IT support: