Comments on: 312. Turbulence. Statistical approach 2

By: NEQNET: last two weeks of March | NEQNET: Non-equilibrium Phenomena

NEQNET: last two weeks of March | NEQNET: Non-equilibrium Phenomena — Thu, 02 Apr 2009 14:56:16 +0000

[...] Turbulence: Statistical approach 1 and Turbulence: Statistical approach 2. I discuss statistical treatment of the developed turbulence regime developed by Taylor and [...]

By: 315. Turbulence: order and disorder in turbulent flow

315. Turbulence: order and disorder in turbulent flow — Fri, 20 Mar 2009 14:06:21 +0000

[...] (I hope that you don’t mind, if you do – please let me know ) Last time we have discussed technicalities related to averaging and statistics of the turbulent flow, today I would like to get back to foundations and discuss a bit various structures typically seen [...]

By: Dmitry

Dmitry — Thu, 19 Mar 2009 15:28:04 +0000

Hi Keith,

Sorry for asking about obvious questions (as I often do).

You don’t need to be sorry. Many really good physicists I knew (like Ginzburg) were never afraid to ask stupid questions, that was one of the reasons they knew so much.

Cheers,
Dmitry.

By: Keith C

Keith C — Thu, 19 Mar 2009 14:21:11 +0000

Sorry for asking about obvious questions (as I often do).

“Is it really news that the laws invariant under symmetries still have most solutions being non-invariant under the symmetry?”
Probably I could only solve spherical cows and forget most of the cows are not spherical symmetric. In terms of solving differential equations, probably most of the time the symmetries are broken by initial/boundary conditions.

It is interesting to note that the concept of spontaneous symmetry breaking is so ubiquitous and powerful; not just useful in high energy physics.

Keith

By: Dmitry

Dmitry — Thu, 19 Mar 2009 11:08:04 +0000

Hi Keith,

Lubos has pretty much outlined the answer to your question, but I would also advice you to check out what is spontaneous symmetry breaking.

Regarding simulations – they actually pretty much do, so yes, there is a strong impression that Navier-Stokes is a very good approximation for description of fluids.

Cheers,
Dmitry.

By: Lubos Motl

Lubos Motl — Thu, 19 Mar 2009 05:44:55 +0000

Keith: isn’t it like asking why isn’t your body rotationally invariant under rotations around the z axis even though the laws of Nature are invariant?

Is it really news that the laws invariant under symmetries still have most solutions being non-invariant under the symmetry?

By: Keith C

Keith C — Thu, 19 Mar 2009 01:55:13 +0000

Hi Dmitry
“The Navier-Stokes is scale-invariant.” and the all the physics of the fluid mechanics is captured in Navier-Stokes eq, how can the solution be not scale invariant?
Also, I wonder if simulation agrees well with experiment. If they do, I think we at least know all the physics.

Keith