January & February  2004, 10(1&2): 253-268. doi: 10.3934/dcds.2004.10.253

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

1. 

Department of Mathematics, Texas A&M University, College Station, TX 77843, United States, United States

2. 

Department of Mathematics, Indiana University, Bloomington, IN, 47405, United States

Received  January 2003 Revised  July 2003 Published  October 2003

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.
Citation: C. Foias, M. S Jolly, O. P. Manley. Recurrence in the 2-$D$ Navier--Stokes equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 253-268. doi: 10.3934/dcds.2004.10.253
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