CMS-Flow:Hydro Eqs

Governing Equation

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

        math \frac{\partial h  }{\partial t} + \frac{\partial (h u_j )}{\partial x_j} = S /math

        math \frac{\partial ( h u_i ) }{\partial t} + \frac{\partial (h u_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} + \frac{\partial }{\partial x_j} \biggl[ K_{sa}  h \frac{\partial C_{sa} }{\partial x_j} \biggr \frac{\tau_i }{\rho} ] /math

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