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Accurate Estimation of Third-order Moments from Turbulence Measurements : Volume 16, Issue 1 (17/02/2009)

By Podesta, J. J.

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Book Id: WPLBN0003980686
Format Type: PDF Article :
File Size: Pages 12
Reproduction Date: 2015

Title: Accurate Estimation of Third-order Moments from Turbulence Measurements : Volume 16, Issue 1 (17/02/2009)  
Author: Podesta, J. J.
Volume: Vol. 16, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Forman, M. A., Smith, C. W., Elton, D. C., Gagne, Y., Malécot, Y., & Podesta, J. J. (2009). Accurate Estimation of Third-order Moments from Turbulence Measurements : Volume 16, Issue 1 (17/02/2009). Retrieved from

Description: Space Science Center, University of New Hampshire, Durham, New Hampshire, 03824, USA. 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.

Accurate estimation of third-order moments from turbulence measurements

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