CMS-Flow:Wave Eqs

Wave-action balance equation with diffraction

Taking into account the effect of an ambient horizontal current or wave behavior, CMS-Wave is based on the steady wave-action balance equation (Mase 2001)

        ${\frac {\partial (c_{x}N)}{\partial x}}+{\frac {\partial (c_{y}N)}{\partial y}}+{\frac {\partial (c_{\theta }N)}{\partial \theta }}={\frac {\kappa }{2\sigma }}{\biggl [}(cc_{g}\cos ^{2}\theta N_{y})_{y}-{\frac {cc_{g}}{2}}\cos ^{2}\theta N_{yy}{\biggr ]}-\epsilon _{b}N-S$

for $j=1,2$

        ${\frac {\partial (hU_{i})}{\partial t}}+{\frac {\partial (hU_{i}U_{j})}{\partial x_{j}}}-\epsilon _{ij3}f_{c}U_{j}h=-gh{\frac {\partial \eta }{\partial x_{j}}}-{\frac {h}{\rho _{0}}}{\frac {\partial p_{a}}{\partial x_{j}}}+{\frac {\partial }{\partial x_{j}}}{\biggl (}\nu _{t}h{\frac {\partial U_{i}}{\partial x_{j}}}{\biggr )}+{\frac {\tau _{i}}{\rho }}$  

for $i=1,2$ and $j=1,2$

Symbol	Description
$\sigma$	Wave frequency
$N$	Wave action
$E$	Spectral wave density
$c$	Wave celerity
$c_{g}$	Wave group velocity

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