In a recent paper

The solar wind can be regarded as a network of entangled magnetic flux
tubes and Alfvénic fluctuations propagating within each flux tube

The probability distribution functions (PDFs) of turbulent space
plasmas display sharp peaks and fat tails on small scales within the
inertial subrange

A robust parabolic dependence between the normalized third-order
moment (skewness) and the normalized fourth-order moment (kurtosis)
has been found in local concentrations of contaminants in atmospheric
turbulence as found by

In this paper we investigate the skewness–kurtosis relation during
a triple interplanetary magnetic flux rope (IMFR) event detected by
Cluster-1 in the solar wind. This event was recently characterized by

This paper is organized as
follows. Section

Let

For a Gaussian function

A common way to characterize asymmetry and non-Gaussianity of

A functional relation between the skewness and the kurtosis of

We compute the

In summary, the analysis is described by the following steps:

Compute

Apply the Levenberg–Marquardt algorithm to find

Use

Compute the correlation index

We repeat these steps for

We note that several papers regarding the relation between skewness
and kurtosis have employed the definition of what we refer to as flatness
(Eq.

Figure

This event is characterized by the presence of three interplanetary
magnetic flux ropes. Magnetic flux ropes are magnetic
structures described as bundles of twisted, current-carrying magnetic
field lines bent into a tube-like shape, spiralling around a common
axis

Cluster-1 magnetic field and plasma parameters from
00:00 to 12:00 UT on 2 February 2002. From top to bottom:
modulus of magnetic field

Beginning and end of the intervals depicted in
Fig.

Figure

Timing of the five selected regions during the triple-IMFR event on 2 February 2002.

The

Kurtosis

Figure

The least-square fits of Eq. (

The correlation index

The highest value of the correlation is obtained during

The power spectral density (PSD, left panels) and the
compensated PSD (right panels) for

Next, we investigate the

Probability distribution functions (PDFs) of

The intermittent aspect of interplanetary magnetic field turbulence
can be demonstrated by constructing the PDF of the normalized magnetic-field differences

Next, we analyze the

Figures

Kurtosis

Kurtosis

The least-square fits of Eq. (

Same as in Table

Except for

The highest correlation value for

A theoretical explanation of the parabolic relation between the
skewness and kurtosis of turbulent fluids and plasmas is still an open
question.

Although a theoretical explanation of the

The stochastic model of a time series proposed by

In the previous sections we showed and discussed the value of the
correlation index measuring how well the

In this paper we investigated the relation between the skewness and the
kurtosis during a triple-IMFR event on 2 February 2002. This event was
divided into five regions, namely, the interior of IMFR-1, the interface of
IMFR-1 and IMFR-2, the interior of IMFR-2, the interface of IMFR-2 and
IMFR-3, and the interior of IMFR-3. We then computed the skewness

We also analyzed the

Our findings give support to the conclusion by

All data analyzed in this paper are publicly available via the Cluster Science
Archive at

The authors declare that they have no conflict of interest.

This article is part of the special issue “Space weather
connections to near-Earth space and the atmosphere”. It is a result
of the 6

The authors are grateful to the reviewer for valuable comments. The authors would like to thank Heng Qiang Feng for providing the estimated times of the boundary layers for the three IMFRs observed by Cluster-1. Rodrigo A. Miranda acknowledges support from FAPDF (Brazil) under grant 0193.000984/2015. Adriane B. Schelin acknowledges support from FAPDF under grant 0193.000.884/2015. Abraham C.-L. Chian acknowledges the award of a PVE Distinguished Visiting Professor Fellowship by CAPES (grant no. 88881.068051/2014-01) and the hospitality of Erico Rempel of ITA. José L. Ferreira acknowledges support from the UNIESPAÇO program of the Brazilian Space Agency (AEB), the National Council of Technological and Scientific Development (CNPq), and FAPDF. The topical editor, Alisson Dal Lago, thanks the two anonymous referees for help in evaluating this paper.