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