turbulence and dynamical systems

From: Sanjiv Ramachandran (rsanjiv_at_psu.edu)
Date: 06/27/04 

Date: Sun, 27 Jun 2004 23:01:31 +0000 (UTC)

Hi,
   I am currently reading a book titled `Informal introduction to
Turbulence' by Tsinober (from Tel Aviv University). In the book, the
author has criticized the dynamical systems approach to understand
turbulence. I have a couple of questions. As I am a beginner in this
field
some of these might be elementary.

1. Tsinober says that an essential feature of turbulence is that higher
and higher modes get excited thereby increasing the dimension of the
system, in a state-space sense. Is it supposed to be obvious or is there
good evidence for this ?
In conventional dynamical systems approaches, one usually derives a
low-dimensional which has a fixed number of variables and then tries to
investigate the low-dimensional model to explain turbulence. So,
Tsinober says that this route is not correct.

2. Agreed that low-dimensional models might not always be a faithful
representation of the true picture. But does that necessarily show that
the dynamical systems approach is wrong ? I mean, is dynamical systems
synonymous with low-dimensional models ? I can understand that if the
dimension of the model is not low, it might not be analytically
tractable. But would it not be possible to use something like numerical
continuation on a model which is not necessarily low-dimensional ?

3. This question might sound stupid. If people agree that some phenomena
is described by differential equations and that dynamical systems is the
study of differential equations, where is the controversy ?? Unless of
course, we doubt the validity of the differential equation itself
(Navier-Stokes, in this case).

Please direct your replies to jeeves[AT]psu.edu, not the other id
rsanjiv@psu.edu

The second id is not valid and I am not able to change my email settings
on this newsgroup (or don't know how to do it).

Regards,

Sanjiv Ramachandran,
Graduate Student,
Aerospace Engineering,
Pennsylvania State University. 

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