Shallow viscoplastic flow on an inclined plane

Evolving viscoplastic flows upon slopes are an important idealization of many realistic flows in a variety of geophysical situations where yield stress is thought to play a role: lava dome evolution, levee formation, mudflows, debris flows and ice movement. This is a free surface problem that is not axisymmetric, for non-zero angles of inclination of the slope, and thus one has both the free surface and a fully three dimensional flow field to consider. Here we utilize an asymptotic thin-layer theory to reduce the governing equations to a more manageable form, whilst still retaining the most important physics. This fundamental flow is then explored using both numerical simulations and, in limiting cases, analytic solutions.

Co-authored with N. J. Balmforth and R Sassi

JFM 470, 1--29, 2002