CMS-Flow:Wave-current Interaction: Difference between revisions

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(Created page with '<big> == Wave-current Interaction == 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 …')
 
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<big>
<big>
Under Construction
== Wave-current Interaction ==
== Wave-current Interaction ==
The characteristic velocities  <math>c_x</math>,  <math>c_y</math>, and <math>c_{\theta}</math> are calculated as
The characteristic velocities  <math>c_x</math>,  <math>c_y</math>, and <math>c_{\theta}</math> are calculated as
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     <math>c_y = c_g \sin \theta + V</math>
     <math>c_y = c_g \sin \theta + V</math>
     <math>c_{\theta} = \frac{\sigma}{\sinh 2 k h}
     <math>c_{\theta} = \frac{\sigma}{\sinh 2 k h}
\biggl( \sin \theta \frac{\partial h}{\partial x}  - \cos \theta \frac{\partial h}{\partialy } \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 ^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)


</math>


{| border="1"
{| border="1"
! Symbol !! Description
! Symbol !! Description
|-
| <math> c </math> ||  Wave celerity
|-
| <math> c_g </math> || Wave group velocity
|-
|-
| <math> \sigma </math> || Wave frequency  
| <math> \sigma </math> || Wave frequency  
|-
|-
| <math> N </math> ||  Wave action
| <math> E </math> ||  Spectral wave density
|-
| <math> k </math> ||  Wave number
|-
|-
| <math> E </math> ||  Spectral wave density
| <math> h </math> ||  Total water depth
|-
|-
| <math> c </math> ||  Wave celerity
| <math> U </math> ||  Depth-averaged current velocity in x-direction
|-
|-
| <math> c_g </math> || Wave group velocity
| <math> V </math> || Depth-averaged current velocity in y-direction
|}
|}


Latest 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

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