Wave Radiation Stresses

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

S_{i j} = \int \int E_{w} (f, θ) [n_{g} ω_{i} ω_{j} + δ_{i j} (n_{g} - \frac{1}{2})] d f d θ

(1)

where:

f = the wave frequency [1/s]

θ

= the wave direction [rad]

E_{e}

= wave energy =

1 / 16 ρ g H_{s}^{2}

[N/m]

H_{s}

= significant wave height [m]

w_{i}

= wave unit vector =

(c o s θ, s i n θ)

[-]

δ_{i j} = {\begin{aligned} 1 f o r i = j \\ 0 f o r i \neq j \end{aligned}

n_{g} = \frac{c_{g}}{c} = \frac{1}{2} (1 + \frac{2 k h}{s i n h 2 k n}) [-]

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.

CMS-Wave:Wave Radiation Stresses