title: Inverse statistics of smooth signals: the case of two dimensional turbulence.
abstract: 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.
authors.affiliation: Dipartimento di Fisica and INFM, Università Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy.
authors.forename: L
authors.initials: L
authors.lastname: Biferale
authors.forename: M
authors.initials: M
authors.lastname: Cencini
authors.forename: A
authors.initials: A
authors.lastname: Lanotte
authors.forename: D
authors.initials: D
authors.lastname: Vergni
authors.forename: A
authors.initials: A
authors.lastname: Vulpiani