CMS-Wave:Wave-current Interaction
Jump to navigation
Jump to search
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