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Vorticity statistics in the direct cascade of two-dimensional turbulence
Gregory Falkovich1, Vladimir Lebedev
1Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Abstract:
For the direct cascade of steady two-dimensional (2D) Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. When ϖ is the vorticity coarse-grained over a scale R, the probability density function (PDF), P(ϖ), has a universal asymptotic behavior lnP~-ϖ/ϖ(rms) at ϖ≫ϖ(rms)=[Hln(L/R)](1/3), where H is the enstrophy flux and L is the pumping length. Therefore, the PDF has exponential tails and is self-similar, that is, it can be presented as a function of a single argument, ϖ/ϖ(rms), in distinction from other known direct cascades.
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