CMS-Flow:Hydro Eqs

Governing Equation

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

        ${\frac {\partial h}{\partial t}}+{\frac {\partial (hu_{j})}{\partial x_{j}}}=S$
$forj=1,2$
        ${\frac {\partial (hu_{i})}{\partial t}}+{\frac {\partial (hu_{i}u_{j})}{\partial x_{j}}}-\epsilon _{ij3}f_{c}u_{j}h=g{\frac {\partial \eta }{\partial x_{j}}}+{\frac {1}{\rho _{0}}}{\frac {\partial p_{a}}{\partial x_{j}}}+{\frac {\partial }{\partial x_{j}}}{\biggl [}\nu _{t}h{\frac {\partial u_{i}}{\partial x_{j}}}{\biggr ]}+{\frac {\tau _{i}}{\rho }}$   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.