On the True Nature of Turbulence
Li, Y. Charles
arXiv, 0507254 / Harvested from arXiv
Text on arXiv
In this article, I would like to express some of my views on the nature of turbulence. These views are mainly drawn from the author's recent results on chaos in partial differential equations \cite{Li04}. Fluid dynamicists believe that Navier-Stokes equations accurately describe turbulence. A mathematical proof on the global regularity of the solutions to the Navier-Stokes equations is a very challenging problem. Such a proof or disproof does not solve the problem of turbulence. It may help understanding turbulence. Turbulence is more of a dynamical system problem. Studies on chaos in partial differential equations indicate that turbulence can have Bernoulli shift dynamics which results in the wandering of a turbulent solution in a fat domain in the phase space. Thus, turbulence can not be averaged. The hope is that turbulence can be controlled.
Publié le : 2005-07-13
Classification:  Mathematics - Analysis of PDEs,  Mathematical Physics,  Nonlinear Sciences - Chaotic Dynamics,  Physics - Fluid Dynamics,  76-02, 37-02, 35-02 
@article{0507254,
     author = {Li, Y. Charles},
     title = {On the True Nature of Turbulence},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0507254}
}

Li, Y. Charles. On the True Nature of Turbulence. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0507254/