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Author Topic:  Fractals in turbulence  (Read 474 times)

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Offline Arcadia

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Fractals in turbulence
« on: March 18, 2021, 08:19:40 PM »
Hello dear community,

haven't been here for a long time, I worked a lot on Julia sets until 3 years ago but focused more on university afterwards.
As an engineer mainly working in the field of fluid dynamics I always loved the combination of turbulence and fractals happening due to special vortex structures, energy cascades or other phenomena.

For the first time in my academic period I came across a stunningly beautiful (and horrificly mathematic heavy) paper utilizing a method to yield exponential-order-resolution for some very detailed fluidic fractal-like structures. I would like to give this as a start to gather some other finds you may have discoverd or worked on regarding beautiful or fundamental finds linking both topics.

Here is the link to the paper: https://arxiv.org/abs/1910.10841 - Check out the plots from page 23.

Now it's your turn for interesting finds, I'm curious to see more:

Linkback: https://fractalforums.org/index.php?topic=4101.0

Offline TGlad

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    • Scale symmetry page
Re: Fractals in turbulence
« Reply #1 on: March 19, 2021, 02:04:41 AM »
It's an interesting topic, thanks for the link.

I was going to include some mention of turbulence in my new book (Exploring Scale Symmetry) but it is hard to work out how the scale-invariance fits in.

In 2D the incompressible fluid equations are only scale-invariant when they are inviscid (no viscous term), however it seems almost impossible to generate turbulence in an inviscid fluid because it doesn't distribute energy through the fluid, just flows along in its own little streams smoothly. You need the viscous part for a big vortex to disperse energy into smaller vortices and onwards. But with a viscous term the equations and result are not scale-symmetric.

You can get recursive eddies against a rigid corner (called Moffatt eddies), see pic. This is very suggestive of scale symmetry in a viscous fluid, but the small vortices have disproportionally less energy (speed). So not scale-invariant in space and time.
« Last Edit: March 19, 2021, 02:16:08 AM by TGlad »


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