Appears in collection : 2026 - T2 - WS1 - Vortices and vorticity in geophysical flows

The lake equations arise as a 2D geophysical model describing the vertically averaged evolution of an incompressible inviscid 3D fluid in a domain with spatially varying topography.

We rigorously derive the asymptotic dynamics of point vortices. Specifically, we show that initially sharply concentrated vorticity remains concentrated in a suitable sense. The vortices' trajectories are proven to follow the level lines of the depth function. The result holds for generic concentrated initial data.