Hidden scale invariance in Navier-Stokes intermittency

We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centers. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invaria...

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Bibliographic Details
Published inarXiv.org
Main Authors Mailybaev, Alexei A, Thalabard, Simon
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.07.2021
Subjects
Computational fluid dynamics
Fluid flow
Intermittency
Invariance
Mathematics - Mathematical Physics
Navier-Stokes equations
Physics - Fluid Dynamics
Physics - Mathematical Physics
Rescaling
Scale invariance
Scaling
Symmetry
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Summary:We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centers. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invariance and global temporal scaling onto the same representative flow. At a statistical level, this projection repairs the scale invariance, which is broken by intermittency in the original formulation. Following previous work by the first author, we here postulate and substantiate with numerics that hidden symmetry statistically holds in the inertial interval of fully developed turbulence. We show that this symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers.
ISSN:2331-8422
DOI:10.48550/arxiv.2105.09403