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Hidden scale invariance in Navier-Stokes intermittency.

Alexei A Mailybaev¹, Simon Thalabard¹

¹IMPA, Rio de Janeiro, Brazil.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|January 17, 2022

Summary

A hidden scaling symmetry in the Navier-Stokes equations, related to dynamical spacetime rescaling, is revealed. This symmetry statistically repairs scale invariance broken by intermittency in turbulence.

Keywords:

intermittency symmetries turbulence

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Area of Science:

Fluid dynamics
Turbulence theory
Statistical mechanics

Background:

The Navier-Stokes equations describe fluid motion but exhibit complexities like intermittency.
Scale invariance is a key concept in turbulence, often broken by intermittent phenomena.
Understanding hidden symmetries can unlock new insights into complex physical systems.

Purpose of the Study:

To expose a hidden scaling symmetry within the Navier-Stokes equations in the vanishing viscosity limit.
To investigate how this symmetry impacts the dynamical and statistical properties of fluid flows.
To demonstrate the statistical validity of this hidden symmetry in fully developed turbulence.

Main Methods:

Analysis of Navier-Stokes equations in the vanishing viscosity limit.
Exploitation of dynamical spacetime rescaling around Lagrangian scaling centers.
Numerical substantiation of the hidden symmetry in the inertial interval of turbulence.

Main Results:

A hidden scaling symmetry stemming from dynamical spacetime rescaling was identified.
This symmetry projects Galilean-invariant and globally time-scaled solutions onto a single representative flow.
The hidden symmetry statistically repairs scale invariance, counteracting intermittency effects.

Conclusions:

The hidden scaling symmetry is statistically present in the inertial interval of fully developed turbulence.
This symmetry explains the scale-invariance of specific observables, including Kolmogorov multipliers.
The findings offer a new perspective on turbulence scaling and intermittency.