Shallow free-surface Stokes flow around a corner.

The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of using analytical and numerical methods.

Uncertainty analysis of a model of wind-blown volcanic plumes.

Mathematical models of natural processes can be used as inversion tools to predict unobserved properties from measured quantities. Uncertainty in observations and model formulation impact on the efficacy of inverse modelling. We present a general methodology, history matching, that can be used to investigate the effect of observational and model uncertainty on inverse modelling studies.