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…') |
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big | <big> | ||
== 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} | <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} \biggl[ (c c_g \cos ^2 \theta N_y)_y - \frac{c c_g}{2} \cos ^2 \theta N_{yy} \biggr] | ||
\frac{ | - \epsilon_b N - S </math> | ||
for math j=1,2 /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 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 | </math> | ||
for math i=1,2 /math and math j=1,2 /math | for <math> i=1,2 </math> and <math> j=1,2 </math> | ||
{| border=1 | {| border="1" | ||
! Symbol !! Description | ! Symbol !! Description | ||
|- | |- | ||
| math \sigma /math || Wave frequency | | <math> \sigma </math> || Wave frequency | ||
|- | |- | ||
| math N /math || Wave action | | <math> N </math> || Wave action | ||
|- | |- | ||
| math E /math || Spectral wave density | | <math> E </math> || Spectral wave density | ||
|- | |- | ||
| math c /math || Wave celerity | | <math> c </math> || Wave celerity | ||
|- | |- | ||
| math c_g /math || Wave group velocity | | <math> c_g </math> || Wave group velocity | ||
|} | |} | ||
---- | ---- | ||
/big | </big> | ||
[[CMS#Documentation_Portal | Documentation Portal]] | [[CMS#Documentation_Portal | Documentation Portal]] | ||
Revision as of 22:18, 17 May 2010
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)
![{\displaystyle {\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 }}{\biggl [}(cc_{g}\cos ^{2}\theta N_{y})_{y}-{\frac {cc_{g}}{2}}\cos ^{2}\theta N_{yy}{\biggr ]}-\epsilon _{b}N-S}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/77b39f1a671fb1fcd336f8d8f6ffaec4dbb3c46a)
for
for and
| Symbol | Description |
|---|---|
| Wave frequency | |
| Wave action | |
| Spectral wave density | |
| Wave celerity | |
| Wave group velocity |
