CMS-Flow:Hydro Eqs: Difference between revisions
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- eps_{ij3} f_c u_j h = g \frac{\partial \eta }{\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{1}{\rho_0} \frac{\partial p_a }{\partial x_j} | ||
+ \frac{\partial }{\partial x_j} \biggl[ \mu h \frac{\partial C_{sa} }{\partial x_j} \biggr ] | |||
+ \frac{\tau_i }{\rho} | + \frac{\tau_i }{\rho} | ||
</math> | </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 22:04, 12 May 2010
Governing Equation
The depth-averaged 2-D continuity and momentum equations are given by
![{\displaystyle {\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}}}+{\frac {\partial }{\partial x_{j}}}{\biggl [}\mu h{\frac {\partial C_{sa}}{\partial x_{j}}}{\biggr ]}+{\frac {\tau _{i}}{\rho }}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/6585b80cd0d5bf6ea27f58b6287748c9cfa4c31a)
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.
