Hello to all. Sorry for my english, I'm an italian civil engineering student.
I have a question about the JONSWAP spectrum. We know that the JONSWAP spectrum, in terms of frequency, is:
S(f) = α g[sup]2[/sup] (2π)[sup]-4[/sup] f[sup]-5[/sup] exp {-1.25 (f[sub]m[/sub]/f)[sup]4[/sup]} γ[sup]exp {-(f-f[sub]m[/sub])[sup]2[/sup]/(2σ[sup]2[/sup]f[sub]m[/sub][sup]2[/sup])}[/sup]
Now I would like to write S in term of ω: f= ω/(2π). The first piece of S (f) becomes:
S(ω) = α g[sup]2[/sup] (2π)[sup]-4[/sup] f[sup]-5[/sup] [etc.]
= α g[sup]2[/sup] (2π)[sup]-4[/sup] [ω/(2π)][sup]-5[/sup] [etc.]
= α g[sup]2[/sup] (2π)[sup]-4[/sup] ω[sup]-5[/sup] (2π)[sup]5[/sup] [etc.]
= α g[sup]2[/sup] (2π) ω[sup]-5[/sup] [etc.]
The problem is that in all the books (and also on Wikipedia) it is written:
S (ω) = α g[sup]2[/sup] ω[sup]-5[/sup] [etc.]
without the remaining 2π in my passages. What am I missing?
Thanks for your help!
I have a question about the JONSWAP spectrum. We know that the JONSWAP spectrum, in terms of frequency, is:
S(f) = α g[sup]2[/sup] (2π)[sup]-4[/sup] f[sup]-5[/sup] exp {-1.25 (f[sub]m[/sub]/f)[sup]4[/sup]} γ[sup]exp {-(f-f[sub]m[/sub])[sup]2[/sup]/(2σ[sup]2[/sup]f[sub]m[/sub][sup]2[/sup])}[/sup]
Now I would like to write S in term of ω: f= ω/(2π). The first piece of S (f) becomes:
S(ω) = α g[sup]2[/sup] (2π)[sup]-4[/sup] f[sup]-5[/sup] [etc.]
= α g[sup]2[/sup] (2π)[sup]-4[/sup] [ω/(2π)][sup]-5[/sup] [etc.]
= α g[sup]2[/sup] (2π)[sup]-4[/sup] ω[sup]-5[/sup] (2π)[sup]5[/sup] [etc.]
= α g[sup]2[/sup] (2π) ω[sup]-5[/sup] [etc.]
The problem is that in all the books (and also on Wikipedia) it is written:
S (ω) = α g[sup]2[/sup] ω[sup]-5[/sup] [etc.]
without the remaining 2π in my passages. What am I missing?
Thanks for your help!