Lubrication models of intertial and thin film flows

Abstract: Fluid flows which shallow rapidly often transition from nearly inertial flow, when the flow is deep, to fundamentally dissipative flows, as the flow depth drastically decreases.

This work will explore lubrication models of the inertial to viscous transition, focusing on cases where the free surface behaves elastically in the first instance.

The mathematical tools developed will enable fast and efficient computation of wave runup, and of turbulent dissipation in these scenarios which will inform assessments of rapid erosion. The mathematical framework may also be applied in comparable settings where inertial to viscous flows dominate.