# Can we 'see' the Kolmogorv microscale

My understanding of Kolmogorov Microscale is that in a turbulent fluid, smaller eddies tend to be similiar to larger eddies - until you arrive at the microscale. My understanding (that may be wrong) is that this roughly the smallest eddy in a turbulent flow.

If I'm not wrong, then we should expect to see these 'smallest eddies' in some way. In another question by me about the subject, I was given some numbers for an estimation:

• 100 $\mu m$ for a person running in air
• a range for energy dissipation in ceons that translates 0,1mm to 1cm for the length scale

While small, I imagine one can design an experiment to observe flow at these scales or create a setup (less speed, more viscosity) with larger microscales. Has this been done and can I see pictures?

The answer I believe is no, you cannot see them.

When we talk about eddy sizes, we have to understand that eddies in physical space are all superimposed and we cannot distinguish between them. All of them are stacked together, so at a given point in physical space we will see contributions from all of the eddies measuring from $l$ through $\eta$.

The other thing is that the Kolmogorov length scale is an approximate length determined by scaling laws. There are isotropic eddies smaller, there are ones larger, and there's really a continuum of eddies throughout the entire range. So you couldn't isolate that particular eddy to see it.

• But I would not need to isolate a particular eddy - I'd just need to be sure that there's no eddy smaller than x. Would this not be possible by looking at the shearing of droplets, diffusive mixing or co-moving suspended particles?
– mart
Commented Jul 15, 2014 at 19:09
• @mart If you plotted the sum of multiple sine waves with random frequencies, could you tell from the plot what the highest frequency is? I don't think you can and it's the same issue here. Commented Jul 15, 2014 at 19:21
• flow is no numbers game, it's a mechanical thing with mechanical effects. Obviously we both don't know, but I don't think your analogy holds.
– mart
Commented Jul 15, 2014 at 19:23

Bare with me but I am doing a little test:

I imagine it should be this http://navier.stanford.edu/thermosciences/TSD-151.pdf figure 4.16 / 4.17 gives vortexes, and fig 4.22 / 4.23 gives how much there is dissipation.

Note There is quite a set of not so easy content to go through, before arriving to the pictures.

PS: It would help if somebody else with more insights can double check this answer.

• I've only skimmed the paper to see the figures you mentioned. They show a vorticity contour plot, isn't the vorticity 'simply' the rotation at a given location? Does this tell us anything about the size of the eddy?
– mart
Commented Jun 11, 2014 at 7:27
• That is an x,y plot over 10 time points, therefore "round vortexes" that you see in more intense colors are done for the same purpose to show that there is rotation there, vorticity is the curl of the speed field (and the vortex may be a complex whirl not necessarly a nice round shape). Where it gets more interesting is the dissipation pictures, that should show which area / vortexes are dissipating more. Therefore you see high intense dissipation around the particle, and that some vortexes are not reflected in the dissipation diagram (i.e. those ones are not really doing the dissipation). Commented Jun 11, 2014 at 11:05
• The size of the eddie is the average / effective size of the turbulent area. Commented Jun 11, 2014 at 11:09
• Still I am not at all an expert, some reading of this paper and some standard bibliographic research would give a better insight than what I can do in this context. This was for me a test to check reactiveness of senior users in the forum which I don't see much. The test required me some 30 min of searches, but it would require to me at least a couple of weeks of full time reading to get some decent clue (and there is at least one senior user that has a better clue than what I currently do). Commented Jun 11, 2014 at 11:14
• I'm not 100% sure what you tried to test, I appreciate the effort in answering my question and I'll think about your answer some more
– mart
Commented Jun 11, 2014 at 13:03