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)

        $\frac{\partial (c_{x}N)}{\partial x}+\frac{\partial (c_{y}N)}{\partial y}+\frac{\partial (c_{\theta }N)}{\partial \theta }=\frac{\kappa }{2\sigma }[(c{c}_g{\cos }^2\theta N_y{)}_y-\frac{c{c}_g}{2}{\cos }^2\theta N_{yy}]-{ϵ}_{b}N-S$

for $j=1,2$

        $\frac{\partial (h{U}_i)}{\partial t}+\frac{\partial (h{U}_i{U}_j)}{\partial x_j}-{ϵ}_{ij3}{f}_c{U}_{j}h=-gh\frac{\partial \eta }{\partial x_j}-\frac{h}{{\rho }_0}\frac{\partial p_a}{\partial x_j}+\frac{\partial }{\partial x_j}\left({\nu }_{t}h\frac{\partial U_i}{\partial x_j}\right)+\frac{{\tau }_i}{\rho }$  

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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