Rigorous remarks about scaling laws in turbulent fluids

Hairer, Martin; Gubinelli, Massimiliano; Flandoli, Franco; Romito, Marco

Hairer, Martin; Gubinelli, Massimiliano; Flandoli, Franco; Romito, Marco (2008), Rigorous remarks about scaling laws in turbulent fluids, Communications in Mathematical Physics, 278, 1, p. 1-29. http://dx.doi.org/10.1007/s00220-007-0398-9

Type

Article accepté pour publication ou publié

Date

2008

Journal name

Communications in Mathematical Physics

Volume

278

Number

Publisher

Springer

Pages

1-29

Abstract (EN)

A definition of 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 the 3D stochastic Navier-Stokes equations, necessary and sufficient conditions for scaling laws to hold are given, translating the problem into bounds for energy and enstrophy of high and low modes respectively. Unlike in the 2D case, the validity or invalidity of such conditions in 3D remains open.

Subjects / Keywords

Mathematics; Probability