CMS-Wave:Wave-current Interaction

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Under Construction

Wave-current Interaction

The characteristic velocities c_x, c_y, and c_{\theta} are calculated as

  c_x = c_g \cos \theta + U (1)
  c_y = c_g \sin \theta + V (2)
c_{\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} 

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
 c Wave celerity
 c_g Wave group velocity
 \sigma Wave frequency
 E Spectral wave density
 k Wave number
 h Total water depth
 U Depth-averaged current velocity in x-direction
 V Depth-averaged current velocity in y-direction

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