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Hidden scale invariance in Navier-Stokes intermittency.
Alexei A Mailybaev1, Simon Thalabard1
1IMPA, Rio de Janeiro, Brazil.
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.
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.
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