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

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Under Construction
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
 
{{Equation|<math>c_x = c_g \cos \theta + U </math>|1}}
\begin{equation} c_x = c_g \cos \theta + U \end{equation}
{{Equation|<math>c_y = c_g \sin \theta + V </math>|2}}
\begin{equation} c_y = c_g \sin \theta + V \end{equation}    
{{Equation|<math>
\begin{equation} c_{\theta} = \frac{\sigma}{\sinh 2 k h}
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}  
\end{equation}    
</math>|3}}


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)


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[[CMS#Documentation_Portal | Documentation Portal]]
[[CMS#Documentation_Portal | Documentation Portal]]

Revision as of 15:42, 22 October 2012

Under Construction

Wave-current Interaction

The characteristic velocities , , and are calculated as

  (1)
  (2)
  (3)

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

Documentation Portal

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