ESTIMATION OF UNIVERSAL MULTIFRACTAL INDICES FOR ATMOSPHERIC TURBULENT VELOCITY FIELDS

We study wind turbulence with the help of universal multifractals, using atmospheric high resolution time series. We empirically determine the three universal indices (H, C(1), and alpha) 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 approximate to 1/3, while C(1) corresponds to the inhomogeneity of the mean field (C(1) = 0 for homogeneous fields, and C(1) > 0 for inhomogeneous and intermittent fields). The most important index is the Levy index a corresponding to the degree of multifractality (0 <= alpha <= 2, alpha = 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: alpha approximate to 1.45 +/- 0.1 and C(1) approximate to 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 (alpha >= 1) processes. This describes the entire hierarchy of singularities of the Navier-Stokes equations.