A model differential equation for turbulence
Abstract
A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is presented. This equation respects the scaling properties of the original Navier-Stokes equations and it has the Kolmogorov -5/3 cascade and the thermodynamic equilibrium spectra as exact steady state solutions. The general steady state in this model contains a nonlinear mixture of the constant-flux and thermodynamic components. Such "warm cascade" solutions describe the bottleneck phenomenon of spectrum stagnation near the dissipative scale. Self-similar solutions describing a finite-time formation of steady cascades are analysed and found to exhibit nontrivial scaling behaviour.
Cite
@article{arxiv.physics/0304044,
title = {A model differential equation for turbulence},
author = {Colm Connaughton and Sergey Nazarenko},
journal= {arXiv preprint arXiv:physics/0304044},
year = {2007}
}
Comments
April 10 2003 Updated April 22 2003, 9 pages revtex4, 9 figures Added some figures, additional references and corrected typos