# Integral Length Scale - 2D

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 May 15, 2018, 07:05 Integral Length Scale - 2D #1 New Member   Join Date: May 2017 Posts: 10 Rep Power: 9 Hello Everyone, I want to calculate the integral length scale directly from the energy spectrum. According to Wiki (https://en.wikipedia.org/wiki/Integral_length_scale) this can be done via But I am working on 2D-flows and I have reason to suspect, that this formula should include a factor of 2 in this case, though I couldn't find anything about this. Does anyone know whether there is indeed a factor of 2 or if I am mistaken? Thanks a lot and greetings

 May 16, 2018, 03:09 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,793 Rep Power: 71 What is your specific reasoning for the factor 2 in 2D? Actually, my opinion is that any evalution of the integral lenght is for the order of magnitude, so that a factor of 2 would not change so much. See https://www.researchgate.net/publica...Numerical_Data

 May 16, 2018, 03:48 #3 New Member   Join Date: May 2017 Posts: 10 Rep Power: 9 I used a gaussian Spectrum with . I calculated the longitudinal correlation function via . In this case I obtained . The integral length scale is the integral over the correlation function . But if I calculate the same quantity via the method in my first post, I get .

 May 17, 2018, 22:52 #4 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,688 Rep Power: 66 These formulae look quite arbitrary. What is the result for 3D?

 May 18, 2018, 10:46 #5 New Member   Join Date: May 2017 Posts: 10 Rep Power: 9 I'm sorry, but I do not understand. What do you think is arbitrary?

 May 19, 2018, 16:56 #6 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,793 Rep Power: 71 I think you could start by the general definition in terms of the integral of the autocorrelation, considering that spectra and correlation are related each other by direct/inverse Fourier transformation. But in general the determination of the integral scale is somehow still debated, as you can see for example here http://www.turbulence-online.com/Pub...apers/WG02.pdf

 Tags integral length scale, length scale, two dimensional