CMS-Flow:Hydro Eqs

Governing Equation

The depth-averaged 2-D continuity and momentum equations are given by

        $\frac{\partial h}{\partial t}+\frac{\partial (h{u}_j)}{\partial x_j}=S$
$forj=1,2$
        $\frac{\partial (h{u}_i)}{\partial t}+\frac{\partial (h{u}_i{u}_j)}{\partial x_j}-{ϵ}_{ij3}{f}_c{u}_{j}h=g\frac{\partial \eta }{\partial x_j}+\frac{1}{{\rho }_0}\frac{\partial p_a}{\partial x_j}+\frac{\partial }{\partial x_j}\left[{\nu }_{t}h\frac{\partial u_i}{\partial x_j}\right]+\frac{{\tau }_i}{\rho }$   for $i=1,2$ and $j=1,2$

where $t$ is time, $u_j$ is the current velocity in the jth direction, $h$ is the total water depth, $C_{sa}$ is the salinity concentration, and $K_{sa}$ is the salinity mixing coefficient.