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> | |||
for <math> j=1,2 </math> | |||
<math> \frac{\partial ( h u_i ) }{\partial t} + \frac{\partial (h u_i u_j )}{\partial x_j} | <math> \frac{\partial ( h u_i ) }{\partial t} + \frac{\partial (h u_i u_j )}{\partial x_j} | ||
- \epsilon_{ij3} f_c u_j h = g \frac{\partial \eta }{\partial x_j} | - \epsilon_{ij3} f_c u_j h = g \frac{\partial \eta }{\partial x_j} | ||
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+ \frac{\partial }{\partial x_j} \biggl[ \nu_t h \frac{\partial u_i }{\partial x_j} \biggr ] | + \frac{\partial }{\partial x_j} \biggl[ \nu_t h \frac{\partial u_i }{\partial x_j} \biggr ] | ||
+ \frac{\tau_i }{\rho} | + \frac{\tau_i }{\rho} | ||
</math> | </math> | ||
for <math> i=1,2 </math> and <math> j=1,2 </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 22:12, 12 May 2010
Governing Equation
The depth-averaged 2-D continuity and momentum equations are given by
for
for and
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.