A multifractal formalism for vector-valued random fields based on wavelet analysis application to turbulent velocity and vorticity 3D numerical data文档.pdf

Stoch Environ Res Risk Assess (2008) 22:421–435 DOI 10.1007/s00477-007-0121-6 ORIGINAL PAPER A multifractal formalism for vector-valued random fields based on wavelet analysis: application to turbulent velocity and vorticity 3D numerical data Pierre Kestener Æ Alain Arneodo Published online: 24 April 2007 Springer-Verlag 2007 Abstract Extreme atmospheric events are intimately re- intermittent than previously estimated from longitudinal lated to the statistics of atmospheric turbulent velocities. and transverse velocity increment statistics. These, in turn, exhibit multifractal scaling, which is determining the nature of the asymptotic behavior of velocities, and whose parameter evaluation is therefore of great interest currently. We combine singular value 1 Introduction decomposition techniques and wavelet transform analysis to generalize the multifractal formalism to vector-valued Several studies over the last decade have shown that random fields. The so-called Tensorial Wavelet Transform atmospheric extremes are subject to multifractal scaling Modulus Maxima (TWTMM) method is calibrated on (Hubert et al. 1993; Burlando and Rosso 1996; Bendjoudi synthetic self-similar 2D vector-valued multifractal mea- et al. 1997; Veneziano and Furcolo 2002; De Michele et al. sures and monofractal 3D vector-valued fractional 2002; Castro et al. 2004), a finding that is heuristically Brownian fields. We report the results of some application supported by the multifractality found in chaotic dynamical of the TWTMM method to turbulent velocity and vorticity systems in general (Halsey et al. 1986; Collet et al. 1987; fields generated by direct numerical simulations of the Rand 1989), a