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.
By Geoffrey Vallis
By Luca Melzi
By Beatrice Pelloni
