CMS-Wave:Wave-current Interaction: Difference between revisions
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(Created page with 'big Under Construction == Wave-current Interaction == The characteristic velocities mathc_x/math, mathc_y/math, and mathc_{\theta}/math are calculated as …') |
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Under Construction | Under Construction | ||
== Wave-current Interaction == | == Wave-current Interaction == | ||
The characteristic velocities | The characteristic velocities <math>c_x</math>, <math>c_y</math>, and <math>c_{\theta}</math> are calculated as | ||
<math>c_x = c_g \cos \theta + U</math> | |||
<math>c_y = c_g \sin \theta + V</math> | |||
<math>c_{\theta} = \frac{\sigma}{\sinh 2 k h} | |||
\biggl( \sin \theta \frac{\partial h}{\partial x} - \cos \theta \frac{\partial h}{\partial y } \biggr) | \biggl( \sin \theta \frac{\partial h}{\partial x} - \cos \theta \frac{\partial h}{\partial y } \biggr) | ||
+ \cos \theta \sin \theta \frac{\partial U}{\partial x} | + \cos \theta \sin \theta \frac{\partial U}{\partial x} | ||
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+ \sin ^2 \theta \frac{\partial V}{\partial x} | + \sin ^2 \theta \frac{\partial V}{\partial x} | ||
- \cos \theta \sin \theta \frac{\partial V}{\partial y} | - \cos \theta \sin \theta \frac{\partial V}{\partial y} | ||
/math | </math> | ||
The dispersion relationships between the relative angular frequency σ, the absolute angular frequency ω, the wave number vector k, and the current velocity vector U = U2 +V2 are (Jonsson 1990) | The dispersion relationships between the relative angular frequency σ, the absolute angular frequency ω, the wave number vector k, and the current velocity vector U = U2 +V2 are (Jonsson 1990) | ||
{| border=1 | {| border="1" | ||
! Symbol !! Description | ! Symbol !! Description | ||
|- | |- | ||
| math c /math || Wave celerity | | <math> c </math> || Wave celerity | ||
|- | |- | ||
| math c_g /math || Wave group velocity | | <math> c_g </math> || Wave group velocity | ||
|- | |- | ||
| math \sigma /math || Wave frequency | | <math> \sigma </math> || Wave frequency | ||
|- | |- | ||
| math E /math || Spectral wave density | | <math> E </math> || Spectral wave density | ||
|- | |- | ||
| math k /math || Wave number | | <math> k </math> || Wave number | ||
|- | |- | ||
| math h /math || Total water depth | | <math> h </math> || Total water depth | ||
|- | |- | ||
| math U /math || Depth-averaged current velocity in x-direction | | <math> U </math> || Depth-averaged current velocity in x-direction | ||
|- | |- | ||
| math V /math || Depth-averaged current velocity in y-direction | | <math> V </math> || Depth-averaged current velocity in y-direction | ||
|} | |} | ||
---- | ---- | ||
/big | </big> | ||
[[CMS#Documentation_Portal | Documentation Portal]] | [[CMS#Documentation_Portal | Documentation Portal]] | ||
Revision as of 21:56, 8 September 2011
Under Construction
Wave-current Interaction
The characteristic velocities , , and are calculated as
The dispersion relationships between the relative angular frequency σ, the absolute angular frequency ω, the wave number vector k, and the current velocity vector U = U2 +V2 are (Jonsson 1990)
| Symbol | Description |
|---|---|
| Wave celerity | |
| Wave group velocity | |
| Wave frequency | |
| Spectral wave density | |
| Wave number | |
| Total water depth | |
| Depth-averaged current velocity in x-direction | |
| Depth-averaged current velocity in y-direction |
