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- Title
ESTIMATION OF UNIVERSAL FOR ATMOSPHERIC TURBULENT MULTIFRACTAL INDICES VELOCITY FIELDS.
- Authors
SCHMITT, F.; SCHERTZER, D.; LOVEJOY, S.; BRUNET, Y.
- Abstract
We study wind turbulence with the help of universal multifractals, using atmospheric high resolution time series. We empirically determine the three universal indices (H, C1, and α) which are sufficient to characterize the statistics of turbulence. The first, H, which characterizes the conservation of the field, is theoretically and empirically known to be ≈1/3, while C1 corresponds to the inhomogeneity of the mean field (C1=0 for homogeneous fields, and C1>0 for inhomogeneous and intermittent fields). The most important index is the Lévy index α corresponding to the degree of multifractality (0≤α≤2, α=0 for a monofractal). The two latter indices are directly obtained by applying the double trace moment technique (DTM) on the turbulent field. Analyzing various atmospheric velocity measurements we obtain: α≈1.45±0.1 and C1≈0.25±0.1. These results show that atmospheric turbulence has nearly the same multifractal behavior everywhere in the boundary layer, corresponding to unconditionally hard multifractal (α≥1) processes. This describes the entire hierarchy of singularities of the Navier-Stokes equations.
- Publication
Fractals, 1993, Vol 1, Issue 3, p568
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X93000599