Statistics or Probability Distribution Functions (PDFs) of magnetic field and velocity variations are important to the study of turbulence. Their scale-dependent departure from Gaussianity on short spatial separation scales (see Figure 1) has long been recognized and ascribed to intermittency, so much so that intermittency is now identified with that departure from Gaussianity. Intermittency itself, however, remains loosely defined and much of a mystery. Its physical nature and mechanism are still very much open questions, as is the cause of the non-Gaussian PDFs of field variations.

Phase correlation is often believed to be the cause of the non-Gaussian PDFs, and of the coherent structures (e.g., vortices) associated with them. The concept of spectral variability, however, is also naturally associated with intermittency. Though difficult to measure in the inertial range of hydrodynamic or fluid turbulence, variability can clearly be measured in the inertial range of solar wind 

turbulence, over orders of magnitude, both in scale and amplitude, through the fluctuations of the spectral level of turbulence (see Figures 2 & 3) and their distribution function Q. A central question therefore is: which of the phase correlation or the spectral variability is the main cause of the observed non-Gaussian PDFs of field variations? The main objective of the work funded under this grant was to answer this question through theory/modeling of the non-Gaussian PDFs and data analysis of the SW turbulence, using data from the ACE, Wind and  Helios 2 spacecraft.

We clearly find (and demonstrate) that phase correlations are not to be blamed for the observed non-Gaussian PDFs. We clearly demonstrate that in the SW, time variability of the power level of turbulence is the cause of the non-Gaussian PDFs, not the phase correlations.

Through modeling along a SW flow line of the self-similar field variations, in a simple ``constant-at-all-scales'' Fourier spectrum of magnetic turbulence, and convolution of these field variations with the measured distributions Q of the time-varying Fourier power levels, we obtain accurate fits of the measured non-Gaussian PDFs of magnetic field variations over a very broad range of inertial scales in the SW (shown in Figure 1 for scales of 1e9, 1e10 and 1e11cm). The modeling of the self-similar fields assumes no phase correlation. Because this random-phases model produces, after convolution with Q, PDFs that match the observed non-Gaussian PDFs well, we conclude that the non-Gaussianity of the observed PDFs is not caused by phase correlations between the components of the turbulence. This of course does not exclude the possibility of phase correlations. Phase correlation has been demonstrated in the SW turbulence. It just precludes phase correlations as the main explanation for the non-Gaussianity. The obvious explanation that arises from our modeling is the time variability of the power level.

Modeling with split distributions Q of power levels, separating the effects of high, intermediate and low power levels, further shows that the PDF tails are produced by the high power levels. Another test consisting in randomizing the phases of the power spectra measured on series of subintervals with decreasing lengths, and in computing the PDFs of the field variations obtained from the inverse Fourier transforms of these randomized-phases spectra, demonstrates how the PDFs converge toward the non-Gaussian PDFs of the original data as the length of the subintervals is decreased (see Figure 4), allowing again the capture of the time-variations in the power levels.

We also find that inertial-range intermittency is much stronger in SW turbulence than it is in terrestrial fluid turbulence. We suspect that mechanisms of significantly different nat...

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