Shallow water equations

For a one-layer fluid
${\frac {\partial h}{\partial t}}+\nabla \cdot \left(h\mathbf {u} \right)=0\,,$
${\frac {\partial \mathbf {u} }{\partial t}}+\left(\mathbf {u} \cdot \nabla \right)\mathbf {u} =-g\nabla \eta \,,$
where $h=H+\eta$ is the total depth, H is the mean depth, and $\eta$ is the free-surface displacement.