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On higher-order spectra of turbulence

Published online by Cambridge University Press:  29 March 2006

C. W. Van Atta  and
J. C. Wyngaard
C. W. Van Atta
Affiliation:
Scripps Institution of Oceanography, University of California, La Jolla
J. C. Wyngaard
Affiliation:
Air Force Cambridge Research Laboratories, Bedford, Massachusetts 0173 Present address: Wave Propagation Laboratory, N.O.A.A., Boulder, Colorado 80302.
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Abstract

Measurements of higher-order spectra of turbulent velocity fluctuations in the atmospheric boundary layer over the open ocean and land produce the interesting result that, in the wavenumber range designated originally by Kolmogorov as an inertial subrange, the functional dependence of the spectra on wavenumber is practically independent of the order of the spectrum. These results confirm the observation of Dutton & Deaven that their extension by a dimensional similarity argument of the original Kolmogorov theory to higher-order spectra was not valid. In the present work, we derive an alternative generalization of the Kolmogorov ideas for spectra of arbitrary order. The results of this generalization describe the dependence upon wavenumber of the available data quite well. We also present theoretical calculations based on a Gaussian model for the fluctuating velocity field which furnish quantitative predictions for spectra of arbitrary order that are also in good agreement with the measurements, both in functional form and in absolute value.

Comparison of results based on the Gaussian model with laboratory measurements obtained in a free shear layer shows that the Gaussian theory predicts accurately all the available normalized higher-order spectra for all frequencies. When the corresponding measured higher-order moments are close to those expected for a Gaussian process, the Gaussian theory also correctly predicts the absolute magnitudes of the higher-order spectra.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 4 , 23 December 1975 , pp. 673 - 694
Copyright
© 1975 Cambridge University Press

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