Questions about turbulence spectra

In summary, the conversation discusses measuring a 2D turbulent flow using a split film probe to obtain a time history of the velocity in the x and y directions. 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, giving energy as a function of wave number. The first question asks about the difference between taking a PSD of the total instantaneous velocity versus the fluctuations, and whether the -5/3 slope can still be expected in the inertial range. The second question asks about using a single probe and taking the PSD to get energy as a function of frequency, and whether Taylor's hypothesis must be invoked to see the -5/3 slope. The expert summarizes that
  • #1
RandomGuy88
406
6
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
 
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  • #2
What is a PSD? The power spectral density, I guess.
 
  • #3
RandomGuy88 said:
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.

RandomGuy88 said:
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.
 

1. What is turbulence spectra?

Turbulence spectra refers to the distribution of turbulent energy at different length scales in a turbulent flow. It is a mathematical representation of how energy is transferred from larger eddies to smaller eddies in a turbulent flow.

2. How is turbulence spectra measured?

Turbulence spectra can be measured using various techniques such as hot-wire anemometry, particle image velocimetry, and direct numerical simulations. These techniques involve measuring the velocity fluctuations at different length scales in a turbulent flow.

3. What are the applications of studying turbulence spectra?

Studying turbulence spectra is important for understanding and predicting the behavior of turbulent flows in various engineering and environmental systems. It is also useful for designing more efficient and stable structures, such as aircraft wings or wind turbines, that are subjected to turbulent flow.

4. How does the shape of turbulence spectra vary in different flows?

The shape of turbulence spectra can vary depending on the type of flow. For example, in wall-bounded flows, the spectra have a characteristic shape with a peak at a specific length scale, whereas in free-shear flows, the spectra are more spread out and do not have a distinct peak.

5. What factors affect the shape of turbulence spectra?

The shape of turbulence spectra is affected by various factors such as the type of flow, the Reynolds number, and the type of boundary conditions. Other factors such as the presence of large-scale structures or flow instabilities can also influence the shape of turbulence spectra.

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