CMS-Flow:Hydro Eqs

Governing Equation

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

        ${\frac {\partial h}{\partial t}}+{\frac {\partial (hu_{j})}{\partial x_{j}}}=S$

        ${\frac {\partial (hu_{i})}{\partial t}}+{\frac {\partial (hu_{i}u_{j})}{\partial x_{j}}}-eps_{ij3}f_{c}u_{j}h=g{\frac {\partial \eta }{\partial x_{j}}}+{\frac {1}{\rho _{0}}}{\frac {\partial p_{a}}{\partial x_{j}}}$

Failed to parse (syntax error): {\displaystyle + \frac{\partial }{\partial x_j} \biggl[ K_{sa} h \frac{\partial C_{sa} }{\partial x_j} \biggr \frac{\tau_i }{\rho} ] }

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.