Identifying the multifractal set on which energy dissipates in a turbulent Navier-Stokes fluid

The rich multifractal properties of fluid turbulence illustrated by the work of Parisi and Frisch are related explicitly to Leray's weak solutions of the three-dimensional Navier-Stokes equations. Directly from this correspondence it is found that the set on which energy dissipates, Fm, has a range of dimensions Dm = 3/m (1 < m < oo), and a corresponding range of sub-Kolmogorov dissipation inverse length scales L eta m-1 < Re3/(1+Dm) spanning Re3/4 to Re3. Correspondingly, the multifractal model scaling parameter h, must obey h > hmin with - 23 < hmin < 13.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

The rich multifractal properties of fluid turbulence are related to Leray's weak solutions of the three-dimensional Navier-Stokes equations, as shown by Parisi and Frisch. They found that the set on which energy dissipates, Fm, has dimensions Dm = 3/m (1 < m < oo), and a corresponding range of sub-Kolmogorov dissipation inverse length scales L eta m-1 < Re3/(1+Dm) spanning Re3/4 to Re3. Additionally, the multifractal model scaling parameter h must satisfy h > hmin with -23 < hmin < 13.