Estimating intermittency significance by means of surrogate data: implications for solar wind turbulence - Teodorescu, Eliza; Echim, Marius Mihai; Johnson, Jay (Frontiers in Astronomy and Space Sciences, 2023)
Intermittency is a property of turbulent astrophysical plasmas, such as the solar wind, that implies irregularity and fragmentation leading to non-uniformity in the transfer rate of energy carried by non-linear structures from large to small scales. We evaluate the intermittency level of the turbulent magnetic field measured by the Parker Solar Probe (PSP) in the slow solar wind in the proximity of the Sun, during the probe’s first close encounter. A quantitative measure of intermittency can be deduced from the normalised fourth order moment of the probability distribution functions, the flatness parameter. We calculated the flatness for magnetic field data collected by PSP between November 1 and 9, 2018. We observe that when dividing the data into contiguous time intervals of various lengths, from three to twenty-four hours, the flatness computed for individual intervals differs significantly, suggesting a variation of intermittency, from “quieter” intervals to more intermittent ones. In order to quantify this variability, we apply an elaborate statistical test tailored to identify nonlinear dynamics in a time series. Our approach is based on evaluating the flatness on a set of surrogate data built from the PSP original data such that all nonlinear correlations contained in the dynamics of the signal are eliminated. Nevertheless, the surrogate data are otherwise consistent with the “underlying” linear process, i.e. the null hypothesis that we want to falsify. If a discriminating statistic for the original signal, such as the flatness parameter, is found to be significantly different than that of the ensemble of surrogates, then the null hypothesis is not valid, and we can conclude that the computed flatness reliably reflects the intermittency level of the underlying non-linear processes. We determine that non-stationarity of the time-series strongly influences the flatness of both the data and surrogates and the null hypothesis cannot be falsified. A global fit of structure functions reveals a decrease of flatness at scales smaller than several seconds: intermittency in this scale range is reduced. This behaviour is mirrored by the spectral analysis which is suggestive of an acceleration of the energy cascade at the high frequency end of the inertial regime.