Hidden scale invariance in Navier-Stokes intermittency

TL;DR

This paper reveals a hidden scale invariance in the Navier-Stokes equations at low viscosity, which explains the scale-invariance of turbulence statistics and accounts for intermittency effects.

Contribution

It uncovers a hidden dynamical symmetry in Navier-Stokes equations that restores scale invariance at the statistical level in turbulence.

Findings

Hidden symmetry projects solutions onto a representative flow.

Statistical scale invariance holds in the inertial interval.

Explains the scale-invariance of Kolmogorov multipliers.

Abstract

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.