CMS-Wave:Wave-current Interaction

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)

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

(3)

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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