CMS-Wave:Wave Radiation Stresses

Wave Radiation Stresses

The wave radiation stresses $(S_{ij})$ are calculated using linear wave theory as (Longuet-Higgins and Stewart 1961; Dean and Dalrymple 1984)

$S_{ij}=\int \int E_w(f,\theta )[n_g{\omega }_i{\omega }_j+{\delta }_{ij}(n_g-\frac{1}{2})]dfd\theta$

(1)

where:

f = the wave frequency [1/s]

$\theta$ = the wave direction [rad]

$E_e$ = wave energy = $1/16\rho g{H}_s^2$ [N/m]

$H_s$ = significant wave height [m]

$w_i$ = wave unit vector = $(cos\theta ,sin\theta )$[-]

${\delta }_{ij}=\{\begin{array}{rl}& 1fori=j\\ & 0fori\ne j\end{array}$

---

Documentation Portal

$n_g=\frac{c_g}{c}=\frac{1}{2}(1+\frac{2kh}{sinh2kn})[-]$

$c_g$ = wave group velocity [m/s]

$c$ = wave ce;erotu [m/s]

$k$ = wave number [rad/s]

The wave radiation stresses and their gradients are computed within the wave model and interpolated in space and time in the flow model.