[Falu]

Hey CFD Online-Community,

I have a small question about the wavenumber terminology. In the theory of Kolmogorov, the wavenumber k contains the energy of an eddy and is defined as k=2pi/l . So it has the dimension [1/m]. In a FFT analysis, you transform your time/space-data to the wavenumber domain. This domain is defined as n=f*T/(2pi). Here n is just a number. So I'm assuming, although both variables have the same name, they are not? Or am i getting something wrong here?

Thank you for your help.

[FMDenaro]

Originally Posted by Falu

Hey CFD Online-Community,

I have a small question about the wavenumber terminology. In the theory of Kolmogorov, the wavenumber k contains the energy of an eddy and is defined as k=2pi/l . So it has the dimension [1/m]. In a FFT analysis, you transform your time/space-data to the wavenumber domain. This domain is defined as n=f*T/(2pi). Here n is just a number. So I'm assuming, although both variables have the same name, they are not? Or am i getting something wrong here?

Thank you for your help.

Let me clarify this issue, some assumptions you wrote are not correct in your post.

Assuming l is the Kolomogorov lenght scale, you can say that kl=pi/l is the associated Kolmogorov frequancy. This is a physical frequency [L^-1], nothing to do with any numerical consideration.
If your question is to evaluate the wavenumber (a number) associated to such frequency you have simply to set
kl=nl*2*pi/L -> nl=L/2l

[Falu]

Thanks for the reply. I understand your derivation, but I think the naming is not so clear in the literature. For example, in Pope Chapter 6.1.3:

"Recall from Section 3.7 that' motions of lengthscale t correspond to wavenumber K = 2Pi/l, and that the energy in the wavenumber range(...)"

This would be in your wording the Kolmogorov frequency. But I get your definition and it was my assumption, too. Thank you very much.

[FMDenaro]

Originally Posted by Falu

Thanks for the reply. I understand your derivation, but I think the naming is not so clear in the literature. For example, in Pope Chapter 6.1.3:

"Recall from Section 3.7 that' motions of lengthscale t correspond to wavenumber K = 2Pi/l, and that the energy in the wavenumber range(...)"

This would be in your wording the Kolmogorov frequency. But I get your definition and it was my assumption, too. Thank you very much.

You are right that the nomenclature often used is somehow misleading. I think that the origin this issue is in the fact that is often assumed L=2*pi so that k=n. But k is still dimensional and n is still a number.
Have a look also at 6.4 in Pope