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Turbulence Statistics in a Two-Dimensional Vortex Condensate.

Authors
  • Frishman, Anna1, 2
  • Herbert, Corentin2, 3
  • 1 Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA. , (Jersey)
  • 2 Department of Physics of Complex Systems, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel. , (Israel)
  • 3 Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, Lyon F-69342, France. , (France)
Type
Published Article
Journal
Physical Review Letters
Publisher
American Physical Society
Publication Date
May 18, 2018
Volume
120
Issue
20
Pages
204505–204505
Identifiers
DOI: 10.1103/PhysRevLett.120.204505
PMID: 29864335
Source
Medline
License
Unknown

Abstract

Disentangling the evolution of a coherent mean-flow and turbulent fluctuations, interacting through the nonlinearity of the Navier-Stokes equations, is a central issue in fluid mechanics. It affects a wide range of flows, such as planetary atmospheres, plasmas, or wall-bounded flows, and hampers turbulence models. We consider the special case of a two-dimensional flow in a periodic box, for which the mean flow, a pair of box-size vortices called "condensate," emerges from turbulence. As was recently shown, a perturbative closure describes correctly the condensate when turbulence is excited at small scales. In this context, we obtain explicit results for the statistics of turbulence, encoded in the Reynolds stress tensor. We demonstrate that the two components of the Reynolds stress, the momentum flux and the turbulent energy, are determined by different mechanisms. It was suggested previously that the momentum flux is fixed by a balance between forcing and mean-flow advection: using unprecedently long numerical simulations, we provide the first direct evidence supporting this prediction. By contrast, combining analytical computations with numerical simulations, we show that the turbulent energy is determined only by mean-flow advection and obtain for the first time a formula describing its profile in the vortex.

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