Comments on: 345. Lagrangian turbulence: video of the day

By: Vortex line representation. Cauchy invariant | NEQNET: Non-equilibrium Phenomena

Mon, 13 Apr 2009 10:10:14 +0000

[...] days ago I’ve promised in comments to discuss dynamics of vortex lines in turbulent flows, today is probably a good day to start. And the natural starting point of course is the Kelvin [...]

By: Dmitry

Dmitry — Sat, 11 Apr 2009 18:30:07 +0000

The picture I was talking about is realized in the absence of viscosity (i.e., for Euler), and to understand how viscosity affects it is a great fun. I’ll hopefully talk about this too at some point.

Cheers,
Dmitry.

By: mesterhd

mesterhd — Fri, 10 Apr 2009 22:46:01 +0000

And on the other hand (which seems even more remarkable to me), there exist trajectories such that the tracer will never enter such a dissipative structure.

Interestingly these trajectories eventually determine the statistical properties of the turbulent flow which can be shown explicitly for the case of Burgers turbulence.

By: Dmitry

Dmitry — Fri, 10 Apr 2009 15:05:03 +0000

Actually, yes, and I will eventually write post about this (maybe, next week). The message is this one:

Lagrangian markers never leave their vortex lines – if the given marker belongs to the given line in the very beginning of the evolution, it will always belong to it, and its only degree of freedom is along the vortex line.

It’s funny to understand turbulence in this context, since vortex lines are interacting with each other by Coulomb law. What you see in the end of the video is how one such line is getting really close to the other line with high vorticity.

By: Lubos Motl

Lubos Motl — Fri, 10 Apr 2009 05:49:56 +0000

Is there some more refined message from the video than the observation that small balls are smoothly but randomly moving in 3D that I missed?