The lake equations describe the vertical average velocity in an inviscid incompressible flow of a fluid in a basin whose variable depth \(b : \Omega \to [0, + \infty)\) is small in comparison with the size of its two-dimensional \(\Omega \subset \mathbb{R}^2\) projection. G. Richardson has showed by formal computations that vortices should at the leading order follow level lines of the depth function \(b\). I will present different mathematical results showing the validity of this computation for stationary and time-dependent flows. These results are counterparts of classical results for the vortex dynamics of the Euler equation of inviscid incompressible flows.

This is joint work with Justin Dekeyser (UCLouvain, Louvain-la-Neuve, Belgium).