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# JONSWAP spectum S(w)

## JONSWAP spectum S(w)

(OP)
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 g2 (2π)-4 f-5 exp {-1.25 (fm/f)4} γexp {-(f-fm)2/(2σ2fm2)}

Now I would like to write S in term of ω: f= ω/(2π). The first piece of S (f) becomes:

S(ω) = α g2 (2π)-4 f-5 [etc.]

= α g2 (2π)-4 [ω/(2π)]-5 [etc.]

= α g2 (2π)-4 ω-5 (2π)5 [etc.]

= α g2 (2π) ω-5 [etc.]

The problem is that in all the books (and also on Wikipedia) it is written:

S (ω) = α g2 ω-5 [etc.]

without the remaining 2π in my passages. What am I missing?

### RE: JONSWAP spectum S(w)

So, where did you get your version? Since you're the anomaly... would you argue with MIT? http://web.mit.edu/13.42/www/handouts/wave_spectra...

Nevertheless, since it's in frequency space, it's likely that the putative Fourier transform's form is different, and the pesky 2π is often floating around as a square root term in symmetrical FT's or only in one direction. The only thing you can be certain about with FT is FT-1[FT(f] = f, i.e., the 2π term resolves itself when taking the inverse FT of an FT'd function

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: JONSWAP spectum S(w)

(OP)

#### Quote (IRstuff)

So, where did you get your version?

First of all in original Hasselmann paper (pag. 32). Other references:

• BENASSAI, Introduction to coastal dynamics and shoreline protection, par. 2.2.3 (pag. 100)
• OCHI, Ocean waves, par. 2.3.5 (page 45)
• SORENSEN, Basic wave mechanics for coastal and ocean engineers, par. 6.3.3 (pag. 138)
• USACE, Shore protection manual, vol. 1 (pag. 3-43)

### RE: JONSWAP spectum S(w)

It seems that there is a mistake in the third line. The second line shows f^5 whereas the third line shows the substitution f=w/2n as(w/2n)^-5. the -5 exponent should be a positive exponent unless further substitution in the original equation shows that you are correct.

### RE: JONSWAP spectum S(w)

Note that Pierson-Moskowitz's original paper doesn't have a 2*pi term at all.

The bottom line is that if you can match the graphs, then you're done, regardless of the 2*pi

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: JONSWAP spectum S(w)

(OP)

#### Quote (chicopee)

It seems that there is a mistake in the third line. The second line shows f^5 whereas the third line shows the substitution f=w/2n as(w/2n)^-5. the -5 exponent should be a positive exponent unless further substitution in the original equation shows that you are correct.

Sorry, I didn't understand. For more clarity, I write my passages

#### Quote (IRstuff)

OP's first and second limes are incorrect; it should have f-5 as shown in the cited reference

Sorry, but (again) I didn't find the error you said...

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