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tke(f)=E(f) ???

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Old   June 23, 2019, 15:29
Default tke(f)=E(f) ???
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luca mirtanini
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In a lot of book about turbulence (Pope, Reynolds, Tenneke and Lumley...) there is written this formula that define the spectrum:
\frac{1}{2}(\overline{u^{2}}+\overline{v^{2}}+\overline{w^{2}})=\intE(k)dk (1)

Of course, it could be written as well:
\frac{1}{2}(\overline{u^{2}}+\overline{v^{2}}+\overline{w^{2}})=\intE(f)df (2)

Now, if the (2) is true, starting from the time history of the specific turbulent kinetic energy (let's call it tke(t)), I can do the fft of it

fft(tke(t))= tke(f) (3)

and the tke(f) should be equal to E(f).

Unfortunately, when I apply the formula (2) doing
this formula is not verified (there are a lot of magnitude order of differences).

So I am wandering if I am doing mistake in the theory and which are my mistakes. I hope you can help me
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Old   June 25, 2019, 09:56
Ashish bhigah
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I think that (1) and (2) are correct.
But I notice some problem with the third. Firt of all you need to do a Fourier transform and not a fft which are very different things.
Unfortunately, I am not sure that tke(f) and E(f) are the same thing.
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fft, spectrum, turbulence

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