Open AccessEmerging scale invariance in a model of turbulence of vortices and waves
Author(s) -
Michal Shavit,
Natalia Vladimirova,
Gregory Falkovich
Publication year - 2022
Publication title -
philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.074
H-Index - 169
eISSN - 1471-2962
pISSN - 1364-503X
DOI - 10.1098/rsta.2021.0080
Subject(s) - turbulence , scaling , scale invariance , physics , invariant (physics) , statistical physics , vortex , theoretical physics , limit (mathematics) , amplitude , scale (ratio) , classical mechanics , mathematics , quantum mechanics , mathematical analysis , mechanics , geometry
This note is devoted to broken and emerging scale invariance of turbulence. Pumping breaks the symmetry: the statistics of every mode explicitly depend on the distance from the pumping. And yet the ratios of mode amplitudes, called Kolmogorov multipliers, are known to approach scale-invariant statistics away from the pumping. This emergent scale invariance deserves an explanation and a detailed study. We put forward the hypothesis that the invariance of multipliers is due to an extreme non-locality of their interactions (similar to the appearance of mean-field properties in the thermodynamic limit for systems with long-range interaction). We analyse this phenomenon in a family of models that connects two very different classes of systems: resonantly interacting waves and wave-free incompressible flows. The connection is algebraic and turns into an identity for properly discretized models. We show that this family provides a unique opportunity for an analytic (perturbative) study of emerging scale invariance in a system with strong interactions. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.