Shallow water equations

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