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} | ||
| Line 9: | Line 11: | ||
+ \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
![{\displaystyle {\frac {\partial (hu_{i})}{\partial t}}+{\frac {\partial (hu_{i}u_{j})}{\partial x_{j}}}-\epsilon _{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 [}\nu _{t}h{\frac {\partial u_{i}}{\partial x_{j}}}{\biggr ]}+{\frac {\tau _{i}}{\rho }}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/9328c5a0ccb5025acafac2e5706486958c435707)
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.
