Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

Please welcome our new moderators!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

122 submissions , 103 unreviewed
3,497 questions , 1,172 unanswered
4,543 answers , 19,337 comments
1,470 users with positive rep
407 active unimported users
More ...

Why is there no UV catastrophe (divergence) in turbulence?

+ 6 like - 0 dislike
488 views

I have just read that as the Reynolds number is increased, the separation of macroscopic and microscopic scales increases and that this also means that there is no UV catastrophy (or equivalently UV devergence?) in turbulence.

I do not understand what this means, for example does the increased separation of the macro and microscales just mean that the spectrum is broadening? And what exactly would an UV catastrophe mean in the context of turbulence and how can I see (technically and mathematically) that it does in fact not exist? I have only a rough intuition what it could mean when considering the turbulence problem from a QFT approach, namely that it from this point of view the infinit Reynolds number limit should be renormalizable (?)...

Any comments that would help me to understand what the sentence in the first paragraph exactly means would be appreciated.

asked May 13, 2013 in Theoretical Physics by Dilaton (4,175 points) [ revision history ]

1 Answer

+ 2 like - 0 dislike

It would help to know the context in which you read the phrase you have a problem understanding.

Regarding the scaling vs Reynolds problem, this part is pretty straighforward. The classical statistical theory of turbulence says that the energy cascades from the low wave number modes (typical scale L) to the high wave numbers modes (typical scale µ) where it is dissipated by viscosity.

In a statistical steady state the energy produced at L must be dissipated at µ. Now it is established that L/µ = Re^(3/4). So one clearly sees that as Reynolds increases, µ decreases and is 0 in the infinite Re limit. So this relation can indeed be described (imho misleadingly) by "separation of macro and micro increases".

From the dynamical point of view at infinite Re, the flow becomes inviscid and the Navier Stokes equations are substituted by the Euler equation.

The "UV catastrophy" is more mysterious. Formally one could say that as µ goes to 0, the energy density of the dissipative domain goes to infinity (UV divergence ?). However to that 2 remarks :

1) Navier Stokes is continuous but when µ arrives at molecular scales, the flow is no more continuous and Navier Stokes breaks down.

2) It is true that the spectral energy density increases at high wave numbers. But the nature shows us that there is actually no divergence - you will never see a very small vortice spinning infinitely fast.

This post imported from StackExchange Physics at 2014-03-09 16:19 (UCT), posted by SE-user Stan Won
answered Jun 7, 2013 by Stan Won (90 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverf$\varnothing$ow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...