Horizontal flow convergence ($C=-{\nabla }_h\cdot \mathbf{u}$)

Horizontal flow convergence is the negative horizontal divergence of a velocity field. Positive convergence reduces the horizontal area of a material patch; for constant-depth linear shallow water equations, the surface equation is ${\eta }_t=HC$, so convergence raises the free surface and divergence lowers it. This is a fluid-flow notion, distinct from convergence of a numerical sequence.