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

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  • 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.
    Mathematics Subject Classification: 35Q30, 76F02.


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