Computational modelling of geomorphic mountain flows based on multi-component shallow water theory

The three-year research programme pursues the development of novel modelling tools for the description and prediction of geomorphic mountain flows. The approach is based on a multi-component, shallow layer description of horizontal two-dimensional flow. The overall programme aims to: 1) establish governing equations accounting for the coupled motion of water, liquefied soil, and transported sediment; 2) develop and implement suitable computational techniques; 3) test the equations and computations against theoretical, experimental and field information. As planned in the original proposal, work in the first year has concentrated on the development of the theoretical framework and computational solver. The main theoretical result is a set of general geomorphic flow equations which account for: 1) separate sub-layers having their own density, velocity and rheology; 2) mass and momentum exchanges across sub-layers as well as along and transverse to the flow; 3) modes of support of the granular phase which include contact-load, pore-pressure support, and turbulent suspension. From a computational point of view, the main achievement has been the completion of a second-order accurate, two-dimensional solver for two-layer flows, and its successful application to various geomorphic test cases. The most interesting computation performed to date with the new solver has been the simulation of an evolving field of antidune bedforms. Further revisions to both the theoretical and computational methods will no doubt prove necessary as we proceed. Nonetheless, the basic tools are ready for the next steps planned for the second and third year of the programme. A key part of these efforts will be to carry out detailed comparisons of model results with available laboratory and field data