### 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 language | English (US) |
---|---|

Pages (from-to) | 407-421 |

Number of pages | 15 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 61 |

Issue number | 1 |

State | Published - Jan 2000 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*61*(1), 407-421.

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 61, no. 1, pp. 407-421.

}

TY - JOUR

T1 - Scaling structure of the velocity statistics in atmospheric boundary layers

AU - Kurien, Susan

AU - L'vov, Victor S.

AU - Procaccia, Itamar

AU - Sreenivasan, K. R.

PY - 2000/1

Y1 - 2000/1

N2 - 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.

AB - 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.

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M3 - Article

VL - 61

SP - 407

EP - 421

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

ER -