Hidden scale invariance in Navier-Stokes intermittency

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.

18 pages, 4 figures

References in corpus (7)

• Burgers Turbulence
• Impact of the floating-point precision and interpolation scheme on the results of DNS of turbulence by pseudo-spectral codes
• Global vs local energy dissipation: the energy cycle of the turbulent von Kármán flow
• Hidden spatiotemporal symmetries and intermittency in turbulence
• Fibonacci turbulence
• Solvable intermittent shell model of turbulence
• A theory of hydrodynamic turbulence based on non-equilibrium statistical mechanics

Cited by in corpus (3)

• Hidden spatiotemporal symmetries and intermittency in turbulence
• Shell model intermittency is the hidden self-similarity
• Spontaneous stochasticity and renormalization group in discrete multi-scale dynamics