Scaling structure of the velocity statistics in atmospheric boundary layers

The statistical objects characterizing turbulence in real turbulent flows d iffer from those of the ideal homogeneous isotropic model. They contain con tributions from various two- and three-dimensional aspects, and from the su perposition of inhomogeneous and anisotropic contributions. We employ the r ecently introduced decomposition of statistical tensor objects into irreduc ible representations of the SO(3) symmetry group (characterized by j and m indices, where j = 0... infinity, -j less than or equal to m less than or e qual to j) to disentangle some of these contributions, separating the unive rsal and the asymptotic from the specific aspects of the how. The different j contributions transform differently under rotations, and so form a compl ete basis in which to represent the tensor objects under study. The experim ental data are recorded with hot-wire probes placed at various heights in t he atmospheric surface layer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of dif ferent contributions to the second order statistical objects characterized by j = 0, 1, and 2. The analysis shows the need to make a careful distincti on between long-lived quasi-two-dimensional turbulent motions (close to the ground) and relatively short-lived three-dimensional motions. We demonstra te that the leading scaling exponents in the three leading sectors (j = 0, 1, and 2) appear to be different but universal, independent of the position s of the probe, the tensorial component considered, and the large scale pro perties. The measured values of the scaling exponent are xi 2((j = 0)) = 0. 68+/-0.01, xi(2)((j = 1)) = 1.0 +/-0.15, and xi(2)((j = 2)) = 1.38+/-0.10. We present theoretical arguments for the values of these exponents using th e Clebsch representation of the Euler equations; neglecting anomalous corre ctions, the values obtained are 2/3, 1, and 4/3, respectively. Some enigmas and questions for the future are sketched. PACS number(s): 47.27.Gs, 47.27 .Jv, 05.40.-a.