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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 16, 99-110, 2009
https://doi.org/10.5194/npg-16-99-2009
© Author(s) 2009. This work is distributed under
the Creative Commons Attribution 3.0 License.
 
17 Feb 2009
Accurate estimation of third-order moments from turbulence measurements
J. J. Podesta1, M. A. Forman2, C. W. Smith1, D. C. Elton3, Y. Malécot4, and Y. Gagne5 1Space Science Center, University of New Hampshire, Durham, New Hampshire, 03824, USA
2Department of Physics and Astronomy, State University of New York, Stony Brook, New York, 11794, USA
3Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York, 12180, USA
4University Joseph Fourier – Grenoble I, BP 53, 38041 Grenoble Cedex 9, France
5Laboratoire des Ecoulements Géophysiques et Industriels, CNRS/UJF/INPG UMR 5519 BP53, 38041 Grenoble, France
Abstract. Politano and Pouquet's law, a generalization of Kolmogorov's four-fifths law to incompressible MHD, makes it possible to measure the energy cascade rate in incompressible MHD turbulence by means of third-order moments. In hydrodynamics, accurate measurement of third-order moments requires large amounts of data because the probability distributions of velocity-differences are nearly symmetric and the third-order moments are relatively small. Measurements of the energy cascade rate in solar wind turbulence have recently been performed for the first time, but without careful consideration of the accuracy or statistical uncertainty of the required third-order moments. This paper investigates the statistical convergence of third-order moments as a function of the sample size N. It is shown that the accuracy of the third-moment <(δ v||)3> depends on the number of correlation lengths spanned by the data set and a method of estimating the statistical uncertainty of the third-moment is developed. The technique is illustrated using both wind tunnel data and solar wind data.

Citation: Podesta, J. J., Forman, M. A., Smith, C. W., Elton, D. C., Malécot, Y., and Gagne, Y.: Accurate estimation of third-order moments from turbulence measurements, Nonlin. Processes Geophys., 16, 99-110, https://doi.org/10.5194/npg-16-99-2009, 2009.
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