Fibonacci Turbulence

Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet deeply connected classes of systems: incompressible hydrodynami...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Natalia Vladimirova, Michal Shavit, Gregory Falkovich
Formato: article
Lenguaje:EN
Publicado: American Physical Society 2021
Materias:
Acceso en línea:https://doaj.org/article/1228c9b462824ec6875181701ce20152
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
id oai:doaj.org-article:1228c9b462824ec6875181701ce20152
record_format dspace
spelling oai:doaj.org-article:1228c9b462824ec6875181701ce201522021-12-02T17:47:01ZFibonacci Turbulence10.1103/PhysRevX.11.0210632160-3308https://doaj.org/article/1228c9b462824ec6875181701ce201522021-06-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021063http://doi.org/10.1103/PhysRevX.11.021063https://doaj.org/toc/2160-3308Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet deeply connected classes of systems: incompressible hydrodynamics and resonantly interacting waves. This work presents the first detailed information-theoretic analysis of turbulence in such strongly interacting systems. The analysis involves both energy and entropy and elucidates the fundamental roles of space and time in setting the cascade direction and the changes of the statistics along it. We introduce a beautifully simple yet rich family of discrete models with triplet interactions of neighboring modes and show that it has quadratic conservation laws defined by the Fibonacci numbers. Depending on how the interaction time changes with the mode number, three types of turbulence were found: single direct cascade, double cascade, and the first-ever case of a single inverse cascade. We describe quantitatively how deviation from thermal equilibrium all the way to turbulent cascades makes statistics increasingly non-Gaussian and find the self-similar form of the one-mode probability distribution. We reveal where the information (entropy deficit) is encoded and disentangle the communication channels between modes, as quantified by the mutual information in pairs and the interaction information inside triplets.Natalia VladimirovaMichal ShavitGregory FalkovichAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021063 (2021)
institution DOAJ
collection DOAJ
language EN
topic Physics
QC1-999
spellingShingle Physics
QC1-999
Natalia Vladimirova
Michal Shavit
Gregory Falkovich
Fibonacci Turbulence
description Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet deeply connected classes of systems: incompressible hydrodynamics and resonantly interacting waves. This work presents the first detailed information-theoretic analysis of turbulence in such strongly interacting systems. The analysis involves both energy and entropy and elucidates the fundamental roles of space and time in setting the cascade direction and the changes of the statistics along it. We introduce a beautifully simple yet rich family of discrete models with triplet interactions of neighboring modes and show that it has quadratic conservation laws defined by the Fibonacci numbers. Depending on how the interaction time changes with the mode number, three types of turbulence were found: single direct cascade, double cascade, and the first-ever case of a single inverse cascade. We describe quantitatively how deviation from thermal equilibrium all the way to turbulent cascades makes statistics increasingly non-Gaussian and find the self-similar form of the one-mode probability distribution. We reveal where the information (entropy deficit) is encoded and disentangle the communication channels between modes, as quantified by the mutual information in pairs and the interaction information inside triplets.
format article
author Natalia Vladimirova
Michal Shavit
Gregory Falkovich
author_facet Natalia Vladimirova
Michal Shavit
Gregory Falkovich
author_sort Natalia Vladimirova
title Fibonacci Turbulence
title_short Fibonacci Turbulence
title_full Fibonacci Turbulence
title_fullStr Fibonacci Turbulence
title_full_unstemmed Fibonacci Turbulence
title_sort fibonacci turbulence
publisher American Physical Society
publishDate 2021
url https://doaj.org/article/1228c9b462824ec6875181701ce20152
work_keys_str_mv AT nataliavladimirova fibonacciturbulence
AT michalshavit fibonacciturbulence
AT gregoryfalkovich fibonacciturbulence
_version_ 1718379511565778944