CMS-Wave:Wave-current Interaction

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Wave-current Interaction

The characteristic velocities $c_x$, $c_y$, and $c_{\theta }$ 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
$c$	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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