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Title: From 2D to 3D in fluid turbulence: unexpected critical transitions

Abstract

How do the laws of physics change with changes in spatial dimension? Maybe not at all in some cases, but in important cases, the changes are dramatic. Fluid turbulence – the fluctuating, intermittent and many-degree-of-freedom state of a highly forced fluid – determines the transport of heat, mass and momentum and is ubiquitous in nature, where turbulence is found on spatial scales from microns to millions of kilometres (turbulence in stars) and beyond (galactic events such as supernovae). When the turbulent degrees of freedom are suppressed in one spatial dimension, the resulting turbulent state in two dimensions (2D) is remarkably changed compared with the turbulence in three dimensions (3D) – energy flows to small scales in 3D but towards large scales in 2D. Although this result has been known since the 1960s due to the pioneering work of Kraichnan, Batchelor and Leith, how one transitions between 3D and 2D turbulence has remained remarkably unexplored. For real physical systems, this is a highly significant question with important implications about transport in geophysical systems that determine weather on short time scales and climate on longer scales. Is the transition from 3D to 2D smooth or are there sharp transitions that signal amore » threshold of the dominance of one type of turbulence over another? Finally, recent results by Benavides & Alexakis (J. Fluid Mech., vol. 822 (2017), pp. 364–385) suggest that the latter may be the case – a surprising and provocative discovery.« less

Authors:
 [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1441304
Report Number(s):
LA-UR-17-26540
Journal ID: ISSN 0022-1120
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 828; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Earth Sciences; Planetary Sciences; Turbulence

Citation Formats

Ecke, R. E. From 2D to 3D in fluid turbulence: unexpected critical transitions. United States: N. p., 2017. Web. doi:10.1017/jfm.2017.507.
Ecke, R. E. From 2D to 3D in fluid turbulence: unexpected critical transitions. United States. doi:10.1017/jfm.2017.507.
Ecke, R. E. Wed . "From 2D to 3D in fluid turbulence: unexpected critical transitions". United States. doi:10.1017/jfm.2017.507. https://www.osti.gov/servlets/purl/1441304.
@article{osti_1441304,
title = {From 2D to 3D in fluid turbulence: unexpected critical transitions},
author = {Ecke, R. E.},
abstractNote = {How do the laws of physics change with changes in spatial dimension? Maybe not at all in some cases, but in important cases, the changes are dramatic. Fluid turbulence – the fluctuating, intermittent and many-degree-of-freedom state of a highly forced fluid – determines the transport of heat, mass and momentum and is ubiquitous in nature, where turbulence is found on spatial scales from microns to millions of kilometres (turbulence in stars) and beyond (galactic events such as supernovae). When the turbulent degrees of freedom are suppressed in one spatial dimension, the resulting turbulent state in two dimensions (2D) is remarkably changed compared with the turbulence in three dimensions (3D) – energy flows to small scales in 3D but towards large scales in 2D. Although this result has been known since the 1960s due to the pioneering work of Kraichnan, Batchelor and Leith, how one transitions between 3D and 2D turbulence has remained remarkably unexplored. For real physical systems, this is a highly significant question with important implications about transport in geophysical systems that determine weather on short time scales and climate on longer scales. Is the transition from 3D to 2D smooth or are there sharp transitions that signal a threshold of the dominance of one type of turbulence over another? Finally, recent results by Benavides & Alexakis (J. Fluid Mech., vol. 822 (2017), pp. 364–385) suggest that the latter may be the case – a surprising and provocative discovery.},
doi = {10.1017/jfm.2017.507},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 828,
place = {United States},
year = {2017},
month = {8}
}

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Figures / Tables:

FIGURE 1 FIGURE 1: Examples of ideal and quasi-2D fluid turbulence that emphasize the role of coherent vortex structures in thin layers: (a) numerical simulation of ideal 2D turbulence (vorticity) (Boffetta & Ecke(2012)), (b) laboratory quasi-2D turbulence (vorticity) (Boffetta & Ecke(2012)), and (c) Atlantic Gulf Stream Eddies (streak image) (Sirah(2012)).

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Works referenced in this record:

Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field
journal, May 2015

  • Gallet, Basile; Doering, Charles R.
  • Journal of Fluid Mechanics, Vol. 773
  • DOI: 10.1017/jfm.2015.232

Two-Dimensional Turbulence
journal, January 2012


Turbulence in More than Two and Less than Three Dimensions
journal, May 2010


Critical transitions in thin layer turbulence
journal, June 2017

  • Benavides, Santiago Jose; Alexakis, Alexandros
  • Journal of Fluid Mechanics, Vol. 822
  • DOI: 10.1017/jfm.2017.293

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.