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Departure from Kolmogorovs -5/3 law

  1. Mar 10, 2013 #1
    I have a time dependent turbulent velocity signal and have computed a power spectral density. What is the significance of the slope, in what appears to be the inertial subrange, not being equal to -5/3? In some regions of the flow the slope is -5/3 but in other regions it is not. In the regions where the slope is not -5/3 the turbulence intensity is considerably less (but not 0) than the regions where the slope is -5/3. I suspect in some of these regions the turbulence is still developing. Could another potential explanation be that because the local turbulence intensities are small, the local turbulence Reynolds number is smaller and therefore the separation between the large scales and the small scales is not sufficient for the inertial subrange to form?

    Also in some of these regions the slope is larger and in some regions it is smaller than -5/3.
  2. jcsd
  3. Mar 10, 2013 #2


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    My "guess" would be that either you are making your measurements in a region where the flow is still transitional or else your measurements themselves are flawed.

    What are you using to make the measurements? If it is a Pitot probe, are you sure you have sufficient frequency response to measure the higher frequencies? If it is a hot wire, is it tuned properly?

    I admittedly don't do a whole lot of work in turbulence, but I have never seen a fully turbulent flow that doesn't obey the -5/3 rule.
  4. Mar 10, 2013 #3
    Thanks for the comments,

    Transitional flow is a definite possibility in these regions and was my first thought. I do not know what a PSD in transitional flow would look like. I would be surprised if there is even a general shape that the PSD would take in transitional flow.

    I am using a hotwire and it is possible that it was not tuned properly.

    The Reynolds number of my flow is 1 million and the turbulence is certainly not isotopic nor homogenous which are assumptions in Kolmogorov's theory. However it is my understanding that even when these assumptions are violated the -5/3 law usually still holds for lower order moments.

    Looks like I have some more investigating to do.
  5. Mar 10, 2013 #4


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    yeah there is no general PSD for a transitional flow. It would depend highly on the type of flow you are measuring and the dominant instability mechanisms at work. For example, on a flat plate, you would start seeing a peak growing at the dominant T-S frequency. As you move farther downstream, you would start seeing harmonics pop up and eventually the signal in between those peaks will start to rise up to form that typical -5/3 spectrum.

    That kind of situation is, in my opinion, the most likely explanation for your observations based on how I've interpreted your original description. That would successfully explain the fact that you are getting lower fluctuations in certain areas than the -5/3 line would predict.

    For the hot wire, calculate the transfer function from running the wire in pulse mode and see where your attenuation starts. That could also be an issue for you, though that would tend to suppress all frequencies to an increasing degree as you get higher in frequency, so it may not really explain what you are seeing. Under certain circumstances, you can have a wire tuned so that it amplifies the signal in the region just before the roll-off as well, so just be careful there.
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