Inverse statistics of smooth signals: the case of two dimensional turbulence.
The problem of inverse statistics (statistics of distances for which the signal fluctuations are larger than a certain threshold) in differentiable signals with power law spectrum, E(k) approximately k(-alpha), 3< or =alpha<5, is discussed. We show that for these signals, with random phases, exit-distance moments follow a bifractal distribution. We also investigate two dimensional turbulent flows in the direct cascade regime, which display a more complex behavior. We give numerical evidences that the inverse statistics of 2D turbulent flows is described by a multifractal probability distribution; i.e., the statistics of laminar events is not simply captured by the exponent alpha characterizing the spectrum.
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Dipartimento di Fisica and INFM, Università Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy.
Cencini
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Lanotte
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Vergni
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Vulpiani
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