I have a set of PLIF images of a passive scalar advected in a turbulent flow. I'm wondering if it's possible to estimate the integral length-scale based on the images of the passive scalar, and if so, how would I go about it. Any references to journal articles about this are welcome.

It seems that a 2D cross-correlation of the images would help, with defined peaks at various length-scales, but then you'd have to filter out a lot of noise.

  • $\begingroup$ Why 2D, 1D would suffice right (unless anisotropy)? So just one row or column of your image set. And what you call noise, isn't that solvable by collecting more statistics? $\endgroup$ – Bernhard Oct 17 '13 at 19:21

It is possible to estb. the length scale of your smallest eddies using a mixture of time-series analyses on some well defined cross-section of your data. Take your 2D images and in the first instance, select a representative section of the flow for which you want to estb. the smallest turbulent length scale or eddie size. From this construct a time series of the value of your scalar field with time in as much detail as you can. Bear in mind here, that if your time step (bin/time-step resolution) is not small enough you will not be able to resolve the smallest turbulent fluctuations and this analysis will not work.

Now, you have a time-series, you can now combine a number of techniques to estb. the an periodicity/quasi-periodicity in the value of the scalar quantity. First, you want to analyse the time-series using a Wavelet transform, this will tell you not only if the time-series contains any periodic fluctuations, but also when they occur in the time-series and on what time-scale. If you see no periodicity here, either there is none (not-likely) or your choice of time-resolution was too large.

Now, for turbulence you are likely to see periodicity at very small time-scale in your wavelet transform (good). But what is turbulence (which can manifest itself as noise shot noise, white noise etc.) and what is flow variability. Well, you now need to establish on what scale noise processes take over macroscopic flow variability - to do this, you can use Structure Function analysis.

Structure function analysis provides a method of quantifying time variability without the problem of aliasing, or windowing, that are encountered using the traditional FFT-based techniques. Potentially it is able to provide information on the nature of the process that causes variability. The method is mainly concerned with the categorization of underlying noise processes and the identification of correlation time-scales. This can then be used to tell you on what scale large variations of the flow cease to be important, this is the scale at which turbulence starts to dominate the energy spectrum.

Now by estimating the dissipation length scale (based upon the the time scale at which noise starts to dominate) and the local sound speed, you are able to calculate a typical time-scale at which turbulence is completely diffused.

I hope this helps.


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