CMS-Flow:Hydro Eqs: Difference between revisions
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(Created page with '== Governing Equation == The depth-averaged 2-D continuity and momentum equations are given by <math> \frac{\partial h }{\partial t} + \frac{\partial (h u_j )}{\partia…') |
(Created page with '== Governing Equation == The depth-averaged 2-D continuity and momentum equations are given by math \frac{\partial h }{\partial t} + \frac{\partial (h u_j )}{\partia…') |
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The depth-averaged 2-D continuity and momentum equations are given by | The depth-averaged 2-D continuity and momentum equations are given by | ||
math \frac{\partial h }{\partial t} + \frac{\partial (h u_j )}{\partial x_j} = S /math | |||
math \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} ] /math | |||
where | 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 22:00, 12 May 2010
Governing Equation
The depth-averaged 2-D continuity and momentum equations are given by
math \frac{\partial h }{\partial t} + \frac{\partial (h u_j )}{\partial x_j} = S /math
math \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} ] /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.