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A correspondence between the multifractal model of turbulence and the Navier-Stokes equations

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Title: A correspondence between the multifractal model of turbulence and the Navier-Stokes equations
Authors: Gibbon, JD
Dubrulle, B
Item Type: Journal Article
Abstract: The multifractal model of turbulence (MFM) and the three-dimensional Navier–Stokes equations are blended together by applying the probabilistic scaling arguments of the former to a hierarchy of weak solutions of the latter. This process imposes a lower bound on both the multifractal spectrum C(h), which appears naturally in the Large Deviation formulation of the MFM, and on h the standard scaling parameter. These bounds respectively take the form: (i) C(h)≥1−3h, which is consistent with Kolmogorov’s four-fifths law ; and (ii) h≥−23. The latter is significant as it prevents solutions from approaching the Navier–Stokes singular set of Caffarelli, Kohn and Nirenberg. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.
Issue Date: 7-Mar-2022
Date of Acceptance: 19-Apr-2021
URI: http://hdl.handle.net/10044/1/89374
DOI: 10.1098/rsta.2021.0092
ISSN: 1364-503X
Publisher: The Royal Society
Journal / Book Title: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume: 380
Issue: 2218
Copyright Statement: © 2022 The Author(s). Published by the Royal Society. All rights reserved.
Keywords: Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
multifractal
Navier-Stokes
intermittency
PARTIAL REGULARITY
INTENSE VORTICITY
SCALING LAWS
REYNOLDS
INTERMITTENCY
DISSIPATION
ONSAGER
FLUID
TUBES
WEAK
Navier–Stokes
intermittency
multifractal
General Science & Technology
Publication Status: Published
Article Number: ARTN 20210092
Online Publication Date: 2022-01-17
Appears in Collections:Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences
Mathematics