CMS-Flow:Hydro Eqs

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Governing Equation

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

        
        Failed to parse (syntax error): {\displaystyle  \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} ] }

where is time, is the current velocity in the jth direction, is the total water depth, is the salinity concentration, and is the salinity mixing coefficient.