Scaling structure of the velocity statistics in atmospheric boundary layers

Susan Kurien, Victor S. L'vov, Itamar Procaccia, K. R. Sreenivasan

Research output: Contribution to journalArticle

Abstract

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 ... ∞, - j ≤m≤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, and 2. The analysis shows the need to make a careful distinction between long-lived quasi-two-dimensional 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(j=0) 2 = 0.68±0.01, ζ(j=1) 2=1.0 ±0.15, and ζ(j=2) 2 = 1.38±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.

Original languageEnglish (US)
Pages (from-to)407-421
Number of pages15
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume61
Issue number1
StatePublished - Jan 2000

Fingerprint

atmospheric boundary layer
Boundary Layer
Probe
statistics
exponents
Scaling
Statistics
scaling
probes
Scaling Exponent
Tensor
Exponent
Enigma
tensors
three dimensional motion
Three-dimensional
Motion
Time Series Data
Symmetry Group
Irreducible Representation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Scaling structure of the velocity statistics in atmospheric boundary layers. / Kurien, Susan; L'vov, Victor S.; Procaccia, Itamar; Sreenivasan, K. R.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 61, No. 1, 01.2000, p. 407-421.

Research output: Contribution to journalArticle

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