20
IRUS TotalDownloads
Altmetric
A correspondence between the multifractal model of turbulence and the Navier-Stokes equations
File | Description | Size | Format | |
---|---|---|---|---|
BD-JDG-RSTA2.pdf | Accepted version | 417.95 kB | Adobe PDF | View/Open |
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 |