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

    $c_x=c_g\cos \theta +U$
    $c_y=c_g\sin \theta +V$
    $c_{\theta }=\frac{\sigma }{\sinh 2kh}(\sin \theta \frac{\partial h}{\partial x}-\cos \theta \frac{\partial h}{\partial y})+\cos \theta \sin \theta \frac{\partial U}{\partial x}-{\cos }^{}\theta \frac{\partial U}{\partial y}+{\sin }^{}\theta \frac{\partial V}{\partial x}-\cos \theta \sin \theta \frac{\partial V}{\partial y}$

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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