345. Lagrangian turbulence: video of the day
Save This Post as PDFA simulation by Guido Bofetta, U. of Torino. Recall that Lagrangian description of hydrodynamics is when you pick a liquid particle and keep track of its motion. Here it is shown how particles are transported by a turbulent flow in the presence of a vortex.
If you liked the post, please kindly consider to leave a comment, subscribe to the RSS feed or get new posts sent directly to your Inbox. If you want to chat with me in real time, you can find me on Twitter. The posts below are probably related to the subject of this one:
5 Comments »
or subscribe me to comments RSS feed
Loading ...
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?
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.
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.
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.