Nonlinear Processes in Geophysics
www.nonlin-processes-geophys.net
1023-5809
1607-7946
16
1
2009
10.5194/npg-16-99-2009
http://www.nonlin-processes-geophys.net/16/99/2009/
http://www.nonlin-processes-geophys.net/16/99/2009/npg-16-99-2009.html
http://www.nonlin-processes-geophys.net/16/99/2009/npg-16-99-2009.pdf
99
110
2009-02-17
Accurate estimation of third-order moments from turbulence measurements
J. J. Podesta
jpodesta@solar.stanford.edu
M. A. Forman
C. W. Smith
D. C. Elton
Y. Malécot
Y. Gagne
Space Science Center, University of New Hampshire, Durham, New Hampshire, 03824, USA
Department of Physics and Astronomy, State University of New York, Stony Brook, New York, 11794, USA
Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York, 12180, USA
University Joseph Fourier – Grenoble I, BP 53, 38041 Grenoble Cedex 9, France
Laboratoire des Ecoulements Géophysiques et Industriels, CNRS/UJF/INPG UMR 5519 BP53, 38041 Grenoble, France
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 <i>N</i>.
It is shown that the accuracy of the third-moment <(δ v<sub>||</sub>)<sup>3</sup>>
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.
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