Remarks on the K41 scaling law in turbulent fluids

F. Flandoli, M. Gubinelli, M. Hairer and M. Romito

First issued 18 July 2005 · PDF

Abstract

A definition of K41 scaling law for suitable families of measures is given and investigated. First, a number of necessary conditions are proved. They imply the absence of scaling laws for 2D stochastic Navier-Stokes equations and for the stochastic Stokes (linear) problem in any dimension, while they imply a lower bound on the mean vortex stretching in 3D. Second, for 3D stochastic Navier-Stokes equations necessary and sufficient conditions for K41 are proved, translating the problem into bounds for energy and enstrophy of high and low modes respectively. The validity of such conditions in 3D remains open. Finally, a stochastic vortex model with such properties is presented.

Versions

1. Version 1 (arXiv v1) current
   18 July 2005
   arXiv comments: 40 pages, 2 figures
   PDF · LaTeX source · files and digests · arXiv:math-ph/0507044

Cite

F. Flandoli, M. Gubinelli, M. Hairer and M. Romito. Remarks on the K41 scaling law in turbulent fluids. Papers of Massimiliano Gubinelli, 2005, version 1. https://mgubi.org/papers/paper/k41-scaling-law/

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