CMS-Wave:Wave-current Interaction: Difference between revisions
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(Created page with '<big> Under Construction == Wave-current Interaction == The characteristic velocities <math>c_x</math>, <math>c_y</math>, and <math>c_{\theta}</math> are calculated as <…') |
(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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big | |||
Under Construction | Under Construction | ||
== Wave-current Interaction == | == Wave-current Interaction == | ||
The characteristic velocities | The characteristic velocities mathc_x/math, mathc_y/math, and mathc_{\theta}/math are calculated as | ||
mathc_x = c_g \cos \theta + U/math | |||
mathc_y = c_g \sin \theta + V/math | |||
mathc_{\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} | ||
| Line 13: | Line 13: | ||
+ \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 | |||
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= | {| border=1 | ||
! Symbol !! Description | ! Symbol !! Description | ||
|- | |- | ||
| | | math c /math || Wave celerity | ||
|- | |- | ||
| | | math c_g /math || Wave group velocity | ||
|- | |- | ||
| | | math \sigma /math || Wave frequency | ||
|- | |- | ||
| | | math E /math || Spectral wave density | ||
|- | |- | ||
| | | math k /math || Wave number | ||
|- | |- | ||
| | | math h /math || Total water depth | ||
|- | |- | ||
| | | math U /math || Depth-averaged current velocity in x-direction | ||
|- | |- | ||
| | | math V /math || Depth-averaged current velocity in y-direction | ||
|} | |} | ||
---- | ---- | ||
/big | |||
[[CMS#Documentation_Portal | Documentation Portal]] | [[CMS#Documentation_Portal | Documentation Portal]] | ||
Revision as of 14:25, 19 May 2010
big Under Construction
Wave-current Interaction
The characteristic velocities mathc_x/math, mathc_y/math, and mathc_{\theta}/math are calculated as
mathc_x = c_g \cos \theta + U/math
mathc_y = c_g \sin \theta + V/math
mathc_{\theta} = \frac{\sigma}{\sinh 2 k h}
\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 ^2 \theta \frac{\partial U}{\partial y} + \sin ^2 \theta \frac{\partial V}{\partial x} - \cos \theta \sin \theta \frac{\partial V}{\partial y}
/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)
| Symbol | Description |
|---|---|
| math c /math | Wave celerity |
| math c_g /math | Wave group velocity |
| math \sigma /math | Wave frequency |
| math E /math | Spectral wave density |
| math k /math | Wave number |
| math h /math | Total water depth |
| math U /math | Depth-averaged current velocity in x-direction |
| math V /math | Depth-averaged current velocity in y-direction |
/big Documentation Portal