Recurrence in the 2-$D$ Navier--Stokes equations

C. Foias; M. S Jolly; O. P. Manley

doi:10.3934/dcds.2004.10.253

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2004, Volume 10, Issue 1&2: 253-268. Doi: 10.3934/dcds.2004.10.253

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Recurrence in the 2-$D$ Navier--Stokes equations

1.
Department of Mathematics, Texas A&M University, College Station, TX 77843
2.
Department of Mathematics, Indiana University, Bloomington, IN, 47405

Received: January 2003

Revised: July 2003

Published: January 2004

Abstract / Introduction Related Papers Cited by

Abstract

Part of the Kolmogorov-Kraichnan-Batchelor theory of turbulence concerns the average enstrophy flux across wave numbers. To support that theory, rigorous relations involving both the net and one-way flux are established using ensemble averages in [9]. In this note we show that some of these relations hold recurrently, and provide explicit estimates for the time intervals of recurrence which are independent of the solution.

Keywords:

Navier-Stokes,
turbulence.

Mathematics Subject Classification: 35Q30, 76F02.

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