PhD Position on Modelling, Analysis and Numerics of Free Surface Flows

In geophysical fluid dynamics, shallow water models are widely used to model free surface flows such as tsunamis, floods, snow or mud avalanches, and atmospheric flows. The equations are derived from the conservation of mass and momentum using the assumptions of small wave amplitudes in comparison to the depth and a constant velocity from the bottom to the top of the water column, which is a severe simplification. Especially in more complex flow situations like avalanches or mudflows, the assumption of a vertically constant velocity profile is wrong. This leads to model errors, e.g., when computing the propagation speed of a snow avalanche or a flood wave generated by a dam break. The goal of this PhD project is the derivation, analysis, and numerical solution of new shallow flow models for geophysical fluid flows. The new models include vertical changes of velocity and will account for complex physical effects such as granular flows and sedimentation. This will allow for efficient and accurate computation of real-world physical processes such as landslides and avalanches.