Questions about turbulence spectra

[RandomGuy88]

I am measuring a 2D turbulent flow using a split film probe. This gives a time history of the velocity in the x and y directions. I have a few questions about obtaining energy spectra from these measurements that I am hoping someone can help me with. The energy spectrum of the turbulent flow is acquired by taking the Fourier transform of the spatial correlation between the fluctuating components of the flow. This gives energy as a function of wave number (length scale).

My first question is: How does this compare to taking a PSD of the total instantaneous velocity (not the fluctuations)? Does a PSD of the instantaneous velocity provide the same information as the energy spectrum of the fluctuations? Can I still expect to see a slope of -5/3 in the inertial range?

Second question: In my experiment I am using a single probe at a fixed location. So I am not able to measure spatial correlations. So by taking the PSD I am actually getting the energy as function of frequency. So can I still expect to see a slope of -5/3 in the inertial range or do I have to invoke Taylor's hypothesis?

Thanks

 

[sams_rhythm]

What is a PSD? The power spectral density, I guess.

 

[boneh3ad]

My first question is: How does this compare to taking a PSD of the total instantaneous velocity (not the fluctuations)? Does a PSD of the instantaneous velocity provide the same information as the energy spectrum of the fluctuations? Can I still expect to see a slope of -5/3 in the inertial range?

The primary difference would be the fact that the total instantaneous velocity would have a nonzero DC component, while the fluctuations would not. Otherwise they should produce the same answer, though the normalized values would be different I suppose.

Second question: In my experiment I am using a single probe at a fixed location. So I am not able to measure spatial correlations. So by taking the PSD I am actually getting the energy as function of frequency. So can I still expect to see a slope of -5/3 in the inertial range or do I have to invoke Taylor's hypothesis?

Keep in mind that I did my PhD work in boundary-layer stability, not turbulence, so I have a lot of experience with power spectra but am still relatively new to turbulence. However, I believe you technically must invoke Taylor's hypothesis, but it is generally a very good approximation in these situations and you end up seeing that -5/3 slope pretty frequently provided that the turbulence is sufficiently developed.