CMS-Flow:Wave Eqs

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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)

        math \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} \frac{\partial (h U_j )}{\partial x_j} = S /math

for math j=1,2 /math

        math \frac{\partial ( h U_i ) }{\partial t} + \frac{\partial (h U_i U_j )}{\partial x_j}

- \epsilon_{ij3} f_c U_j h = - g h \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}
/math  

for math i=1,2 /math and math j=1,2 /math

Symbol	Description
math \sigma /math	Wave frequency
math N /math	Wave action
math E /math	Spectral wave density
math c /math	Wave celerity
math c_g /math	Wave group velocity

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