Probability Density Function of DNS velocity field

Question

I am currently working on a DNS turbulent solver and I would like to compare my IHT simulations to papers. Those papers show the Probability Density Function of the velocity field:

I would like to reproduce this figure from data. I have access to all the velocity fields at any point during the simulation. I don't understand how to compute this PDF from a 3D velocity field or how to take into account all my data.
I don't really know where I am struggling. I suppose it is with the definition of the PDF. I also don't understand the axes on that figure. Why the $x$ axis is $x$ and not the $v_x$ values if we are taking the PDF of the $v_x$?
I tried to mess around with scipy.stats.norm.pdf but I am sure I do not understand how to use it.

causative · Answer

It looks like what they label as $x$ is $v_x$ normalized to have mean 0 and standard deviation 1. It shouldn't be called $x$ really. To get what they call $x$, first you measure a bunch of particle velocities projected onto a single axis of velocity. The velocity of a particle in 3 dimensions would have 3 components and you just take one of them. Then subtract the sample mean and divide by the sample standard deviation. Then apply some sort of smoothing or histogram so you get a frequency curve. The y axis is a little confusing because it's a log-scale plot, which is why you see a quadratic shape instead of a bell curve.

Answered by causative on December 5, 2020

Probability Density Function of DNS velocity field

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