Abstract
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.
Highlights
In the solar wind, coupling between large- and small-scale turbulence occurs at kinetic scales defined by the ion gyroradius and the ion gyro-period
This paper investigates the statistical convergence of third-order moments as a function of the sample size N
We focus on one particular aspect of MHD-scale turbulence which is of some practical importance, namely, the determination of the energy cascade rate from measured data
Summary
In the solar wind, coupling between large- and small-scale turbulence occurs at kinetic scales defined by the ion gyroradius and the ion gyro-period. Theoretical work has shown that plasma heating caused by dissipation of the turbulence can likely explain the observed radial temperature profile of the solar wind which decreases more slowly than would be the case if the expansion were adiabatic (Matthaeus et al, 1996; Zank et al, 1999; Matthaeus et al, 1999; Smith et al, 2001; Isenberg et al, 2003) To refine these theories, accurate measurements of the energy cascade rate are needed. Politano and Pouquet’s law has recently been applied to obtain direct measurements of the energy cascade rate in the solar wind under the simplifying assumption that the turbulence is isotropic (MacBride et al, 2005; Sorriso-Valvo et al, 2007; MacBride et al, 2008; Marino et al, 2008). It should be emphasized that the present study is concerned with algebraic (signed) third-order moments not absolute moments
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