CMS-Flow:Hydro Eqs: Difference between revisions
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<math> \frac{\partial h }{\partial t} + \frac{\partial (h u_j )}{\partial x_j} = S </math> | <math> \frac{\partial h }{\partial t} + \frac{\partial (h u_j )}{\partial x_j} = S </math> | ||
<math> \frac{\partial ( h u_i ) }{\partial t} | <math> \frac{\partial ( h u_i ) }{\partial t} </math> | ||
<math> | |||
+ \frac{\partial (h u_i u_j )}{\partial x_j} | + \frac{\partial (h u_i u_j )}{\partial x_j} | ||
- e_{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> | - e_{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. | 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. | ||
Revision as of 22:02, 12 May 2010
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 u_j )}{\partial x_j} - e_{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.
