power spectrum
 

Assume we have power-frequency spectra from Fourier transform of the auto-correlation at a point in a turbulent field. The question is;

- what kind of information could we get from this energy vs. frequency plot regarding the time/length scales of the flow?

- Does the slope –5/3 for inertial range (as in the wave number K plots) still apply here?

Generally, you can interpret the frequency/wavenumber in which an energy peak appears, as a corresponding physical lenght by simply considering that k = 2pi*n/l

the k^-5/3 slope is theoretical, valid for homogeneous isotropic turbulence... that law does not necessarily appears in general flows ...
For example, in channel flow some appearence of the intertial slope can appear at high Reynolds number in the centerline, that is far from the walls ...

Thanks.

You are right but your arguments are only about wavenumber spectrum. I am wondering about frequency spectrum.

What do you mean? wavenumbers and frequencies are linked, for example

k = n * 2*Pi /L

k : frequency (dimension 1/L)
n : wavenumber (integer)

the same resoning applies for the temporal frequency k_t = n * 2*Pi/T