# The wave direction spreading coefficient

Hi,

I have a question concerning the wave spreading implemented in HydroDyn: As far as I understand the theory behind the cos-2s-spreading function, the wave direction spreading coefficient (s) controls the “concentration” of the directional distribution of the wave energy. A small “s” leads to a relatively wide distribution of wave energy from nearly all directions. A large spreding coefficient centers the energy more to the mean wave direction.

I read about several approches (Mitsuyasu (1975), Hasselmann(1980), Donelan(1985)) where s is frequency dependent and, consequently, the directional spreading function varies over the frequencies as well. E.g.:
s(omega)=s_max*(f/f_p)^5 , if f<f_p and s(omega)=s_max*(f/f_p)^(-2.5), if f>f_p

As far as I understood the directional spreading function in HydroDyn remains constant with the same spreading coeffiencent across all frequencies. Is that right? I tried to find the implementation in the HydroDyn routine, but I’m not sure if I understood it correctly.
Therefore I have to choose a spreading coefficient, which is valid for the directional spreading function across all frequencies of the wave spectrum?

Many thanks in advance and kind regards,

Manuela

Dear Manuela,

Correct. The wave directional spreading is not frequency dependent in FAST/HydroDyn. You can read a bit about the wave-directional spreading model in our OMAE 2014 paper: nrel.gov/docs/fy14osti/61161.pdf.

Best regards,

Thank you for the link to the paper! That is exactly the background information I was looking for.

Best regards,

Manuela