The `lake equation' on a planar domain $D$ with bathymetry $b(x,y)$ is given by $\partial_t u+(u\cdot\operatorname{grad})u=-\operatorname{grad}p$, $\operatorname{div}(bu)=0$, with $u\parallel\partial D$. It is well posed as a PDE, but when $b\neq\mathrm{const}$, justifying point vortex models requires the analyst's attention. We focus on Geometric Mechanics aspects, glossing over hard analysis issues. The motivating example is a `rip current' produced by vortex pairs near a beach shore. For a beach with uniform slope, there is a perfect analogy with Thomson's vortex rings. The stream function produced by a vortex is defined as the Green function of the operator $-\operatorname{div}(\operatorname{grad}\psi/b)$ with Dirichlet boundary conditions. As in elasticity, the lake equations give rise to pseudo-analytical functions and quasi-conformal mappings. Uniformly elliptic equations on close Riemann surfaces could be called `planet equations'.