Inverse statistics of smooth signals: The case of two dimensional turbulence - art. no. 124501

The problem of inverse statistics (statistics of distances for which the si gnal fluctuations are larger than a certain threshold) in differentiable si gnals with power law spectrum, E(k) similar to k(-alpha), 3 less than or eq ual to alpha < 5, is discussed. We show that for these signals, with random phases, exit-distance moments follow a bifractal distribution. We also inv estigate two dimensional turbulent flows in the direct cascade regime, whic h display a more complex behavior. We give numerical evidences that the inv erse statistics of 2D turbulent flows is described by a multifractal probab ility distribution; i.e., the statistics of laminar, events is not simply c aptured by the exponent a characterizing the spectrum.