Applied Mathematics and Plasma Physics

Susan Kurien, Victor S. L'vov, Itamar Procaccia and Katepalli R. Sreenivasan, "Scaling structure of the velocity statistics in atmospheric boundary layers", *Phys. Rev. E*, vol. 61, pp. 407--421, 2000

The statistical objects characterizing turbulence in real
turbulent flows differ from those of the ideal homogeneous
isotropic model. They contain contributions from various two-
and three-dimensional aspects, and from the superposition of
inhomogeneous and anisotropic contributions. We employ the
recently introduced decomposition of statistical tensor objects
into irreducible representations of the SO(3) symmetry group
(characterized by *j* and *m* indices,
where *j = 0...$infty$, -j leq m leq j*) to
disentangle some of these contributions, separating the
universal and the asymptotic from the specific aspects of the
flow. The different *j* contributions transform
differently under rotations, and so form a complete basis in
which to represent the tensor objects under study. The
experimental data are recorded with hot-wire probes placed at
various heights in the atmospheric surface layer. Time series
data from single probes and from pairs of probes are analyzed to
compute the amplitudes and exponents of different contributions
to the second order statistical objects characterized by *j
= 0, 1, 2 *. The analysis shows the need to make a
careful distinction between long-lived quasi-twodimensional
turbulent motions (close to the ground) and relatively
short-lived three-dimensional motions. We demonstrate that the
leading scaling exponents in the three leading sectors
(*j=0, 1, and 2*) appear to be different but
universal, independent of the positions of the probe, the
tensorial component considered, and the large scale
properties. The measured values of the scaling exponent are
*ζ _{2}^{(j=0)}
= 0.68 pm 0.01,
ζ_{2}^{(j=1)} =
1 pm 0.15,
ζ_{2}^{(j=2)} =
1.38 pm 0.10*. We present theoretical arguments for the
values of these exponents using the Clebsch representation of
the Euler equations; neglecting anomalous corrections, the
values obtained are 2/3, 1, and 4/3, respectively. Some enigmas
and questions for the future are sketched.

@article{kurien-2000-scaling,

author = {Susan Kurien and Victor S. L'vov and Itamar Procaccia and Katepalli R. Sreenivasan},

title = {Scaling structure of the velocity statistics in atmospheric boundary layers},

year = {2000},

urlpdf = {http://math.lanl.gov/~skurien/papers/KLPS_aniso_pre00.pdf},

journal = {Phys. Rev. E},

volume = {61},

pages = {407--421}

}