Small-scale universality in fluid turbulence

Jörg Schumacher, Janet D. Scheel, Dmitry Krasnov, Diego A. Donzis, Victor Yakhot, Katepalli R. Sreenivasan

Research output: Contribution to journalArticle

Abstract

Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i ) at Reynolds numbers Re × 102 the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii ) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.

Original languageEnglish (US)
Pages (from-to)10961-10965
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Volume111
Issue number30
DOIs
StatePublished - 2014

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turbulence
fluids
turbulent flow
homogeneous turbulence
Reynolds number
flow geometry
isotropic turbulence
high Reynolds number
low Reynolds number
data simulation
transition points
containers
direct numerical simulation
shear flow
free convection
boxes
energy dissipation
statistics

Keywords

  • Energy dissipation rate
  • Fluid dynamics

ASJC Scopus subject areas

  • General

Cite this

Small-scale universality in fluid turbulence. / Schumacher, Jörg; Scheel, Janet D.; Krasnov, Dmitry; Donzis, Diego A.; Yakhot, Victor; Sreenivasan, Katepalli R.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 111, No. 30, 2014, p. 10961-10965.

Research output: Contribution to journalArticle

Schumacher, Jörg ; Scheel, Janet D. ; Krasnov, Dmitry ; Donzis, Diego A. ; Yakhot, Victor ; Sreenivasan, Katepalli R. / Small-scale universality in fluid turbulence. In: Proceedings of the National Academy of Sciences of the United States of America. 2014 ; Vol. 111, No. 30. pp. 10961-10965.
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