Exact transient solutions for multidimensional flow in unsaturated soil with plant roots

Date(s): Thursday 6th June 2024 (15:00-16:00)
Contact: Event Convenor Contact: Anna.Kalogirou@nottingham.ac.uk
Description: Speaker's Name: Philip Broadbridge
Speaker's Affiliation: La Trobe University (Melbourne, Australia) and IMI-Kyushu University (Kyushu, Japan)
Speaker's Research Theme(s): Fluid mechanics,CMMB
Abstract:
Richards’ equation for flow in an unsaturated soil is a nonlinear diffusion convection equation. In a cropped field, the web of plant roots leads to an additional nonlinear sink term. Before now, the only known exact solutions assumed a sink function that was proportional to the metric flux potential. This gives the wrong convexity for plant water uptake. Now there is a class of nonlinear reaction-diffusion-convection equations that allows a nonclassical symmetry reduction to a linear system. This requires two differential relations among the soil-water diffusivity, hydraulic conductivity and plant root uptake, each being a function of water content. That leaves one free function and a realistic model that can be solved. Solutions are shown for crop uptake from periodic irrigation furrows and from a circular sprinkler.

Venue: Pope A24

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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