CMS-Flow:Wave Eqs: Difference between revisions
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(Created page with '<big> == Wave-action balance equation with diffraction == Taking into account the effect of an ambient horizontal current or wave behavior, CMS-Wave is based on the steady wave-a…') |
(Created page with 'big == Wave-action balance equation with diffraction == Taking into account the effect of an ambient horizontal current or wave behavior, CMS-Wave is based on the steady wave-a…') |
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== Wave-action balance equation with diffraction == | == Wave-action balance equation with diffraction == | ||
Taking into account the effect of an ambient horizontal current or wave behavior, CMS-Wave is based on the steady wave-action balance equation (Mase 2001) | Taking into account the effect of an ambient horizontal current or wave behavior, CMS-Wave is based on the steady wave-action balance equation (Mase 2001) | ||
math \frac{\partial c_x N }{\partial x} | |||
+ \frac{\partial c_y N }{\partial y} | + \frac{\partial c_y N }{\partial y} | ||
+ \frac{\partial c_{\theta} N }{\partial \theta} | + \frac{\partial c_{\theta} N }{\partial \theta} | ||
= \frac{\kappa}{2 \sigma} | = \frac{\kappa}{2 \sigma} | ||
\frac{\partial (h U_j )}{\partial x_j} = S | \frac{\partial (h U_j )}{\partial x_j} = S /math | ||
for | for math j=1,2 /math | ||
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 h \frac{\partial \eta }{\partial x_j} | - \epsilon_{ij3} f_c U_j h = - g h \frac{\partial \eta }{\partial x_j} | ||
- \frac{h}{\rho_0} \frac{\partial p_a }{\partial x_j} | - \frac{h}{\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{\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 | |||
for | for math i=1,2 /math and math j=1,2 /math | ||
{| border= | {| border=1 | ||
! Symbol !! Description | ! Symbol !! Description | ||
|- | |- | ||
| | | math \sigma /math || Wave frequency | ||
|- | |- | ||
| | | math N /math || Wave action | ||
|- | |- | ||
| | | math E /math || Spectral wave density | ||
|- | |- | ||
| | | math c /math || Wave celerity | ||
|- | |- | ||
| | | math c_g /math || Wave group velocity | ||
|} | |} | ||
---- | ---- | ||
/big | |||
[[CMS#Documentation_Portal | Documentation Portal]] | [[CMS#Documentation_Portal | Documentation Portal]] | ||
Revision as of 22:15, 17 May 2010
big
Wave-action balance equation with diffraction
Taking into account the effect of an ambient horizontal current or wave behavior, CMS-Wave is based on the steady wave-action balance equation (Mase 2001)
math \frac{\partial c_x N }{\partial x}
+ \frac{\partial c_y N }{\partial y} + \frac{\partial c_{\theta} N }{\partial \theta} = \frac{\kappa}{2 \sigma} \frac{\partial (h U_j )}{\partial x_j} = S /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}
- \epsilon_{ij3} f_c U_j h = - g h \frac{\partial \eta }{\partial x_j}
- \frac{h}{\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}
/math
for math i=1,2 /math and math j=1,2 /math
| Symbol | Description |
|---|---|
| math \sigma /math | Wave frequency |
| math N /math | Wave action |
| math E /math | Spectral wave density |
| math c /math | Wave celerity |
| math c_g /math | Wave group velocity |
/big Documentation Portal