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 in:arXiv.org 2021-07
Main Authors: Mailybaev, Alexei A, Thalabard, Simon
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Fluid flow
Intermittency
Invariance
Navier-Stokes equations
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