CMS-Wave:Wave-current Interaction: Difference between revisions
m (1 revision: Import from Fault) |
|||
| Line 5: | Line 5: | ||
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 | ||
\begin{equation} c_x = c_g \cos \theta + U \end{equation} | |||
\begin{equation} c_y = c_g \sin \theta + V \end{equation} | |||
\begin{equation} 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} | ||
| 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} | ||
\end{equation} | |||
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) | ||
Revision as of 14:52, 14 September 2011
Under Construction
Wave-current Interaction
The characteristic velocities , , and are calculated as
\begin{equation} c_x = c_g \cos \theta + U \end{equation} \begin{equation} c_y = c_g \sin \theta + V \end{equation} \begin{equation} 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} \end{equation}
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 |
