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The statistical objects characterizing turbulence in real turbulent flowsdiffer from those of the ideal homogeneous isotropic model.Theycontaincontributions from various 2d and 3d aspects, and from the superpositionofinhomogeneous and anisotropic contributions. We employ the recentlyintroduceddecomposition of statistical tensor objects into irreduciblerepresentations of theSO(3) symmetry group (characterized by $j$ and $m$indices), to disentangle someof these contributions, separating the universaland the asymptotic from the specific aspects of the flow. The different $j$contributions transform differently under rotations and so form a completebasis in which to represent the tensor objects under study. The experimentaldata arerecorded with hot-wire probes placed at various heights in theatmospheric surfacelayer. Time series data from single probes and from pairs ofprobes are analyzed to compute the amplitudes and exponents of differentcontributions to the second order statistical objects characterized by $j=0$,$j=1$ and $j=2$. The analysis shows the need to make a careful distinctionbetween long-lived quasi 2d turbulent motions (close to the ground) andrelatively short-lived 3d motions. We demonstrate that the leading scalingexponents in the three leading sectors ($j = 0, 1, 2$) appear to be differentbutuniversal, independent of the positions of the probe, and the largescaleproperties. The measured values of the exponent are $\zeta^{(j=0)}_2=0.68\pm 0.01$, $\zeta^{(j=1)}_2=1.0\pm 0.15$ and $\zeta^{(j=2)}_2=1.38 \pm 0.10$.We present theoretical arguments for the values of these exponents usingtheClebsch representation of the Euler equations; neglecting anomalouscorrections, the values obtained are 2/3, 1 and 4/3 respectively.

Scaling structure of the velocity statistics in atmospheric boundary layers