Effect of Intermittent Structures on the Spectral Index of Magnetic field in the Slow Solar Wind
 ^{1}School of Space and Environment, Beihang University, Beijing, 100083, China
 ^{2}Key Laboratory of Space Environment monitoring and Information Processing of MIIT
 ^{3}School of Electronic Information, Wuhan University, Wuhan, 430072, China
 ^{4}Qian Xuesen Laboratory of Space Technology, Beijing, 100094, China
 ^{1}School of Space and Environment, Beihang University, Beijing, 100083, China
 ^{2}Key Laboratory of Space Environment monitoring and Information Processing of MIIT
 ^{3}School of Electronic Information, Wuhan University, Wuhan, 430072, China
 ^{4}Qian Xuesen Laboratory of Space Technology, Beijing, 100094, China
Abstract. Intermittent structures are ubiquitous in the solar wind turbulence, and they can significantly affect the power spectral index of magnetic field fluctuations which reflects the cascading process of the turbulence. However, the relationship between intermittency magnitude and the spectral index has not been shown yet. Here we present the continuous variation of the magnetic spectral index in the inertial range as a function of the intermittency magnitude. By using the measurements from the WIND spacecraft, we find 42,272 intervals with different levels of intermittency magnitude and with duration of 5–6 minutes from 46 slowwind streams between 2005 and 2013. Among them, each of the intermittent intervals is composed of one dominant intermittent structure and background turbulent fluctuations. For each interval, a spectral index α_{B} is determined for the Fourier spectrum of magnetic field fluctuations in the inertial range between 0.01 Hz and 0.3 Hz. A parameter I_{max}, which corresponds to the maximum of the trace of partial variance increments of the intermittent structure, is introduced as an indicator of the intermittency magnitude. Our statistical result shows that as I_{max} increases from 0 to 20, the magnetic spectrum becomes steeper gradually and the spectral index α_{B} decreases from 1.63 to 2.01. Accordingly, an empirical relation is established between α_{B} and I_{max}. The result will help us to know more details about the contributions of the intermittent structures on the power spectra, and further about the physical nature of the energy cascade taking place in the solar wind. It will also help to improve the turbulence theories that contains intermittent structures.
Xin Wang et al.
Status: open (until 10 Feb 2023)

RC1: 'Comment on angeo202228', Anonymous Referee #1, 14 Dec 2022
reply
The manuscript "Effect of Intermittent Structures on the Spectral Index of Magnetic field in the Slow Solar Wind" by X. Wang and coauthors deals with the investigation of the intermittent properties of solar wind magnetic field fluctuations as measured by the spectral slope of their power spectral density. The paper is well written and the topic is within the scope of ANGEO. However, there are some missing aspects that need to be properly framed out and considered before it can be accepted for publication.
Major comments
 The paper accounts for finding a relationship between the spectral exponent and the level of intermittency in slow solar wind streams observed at 1 AU by WIND. The results shown in the paper are not new since a close correspondence between intermittency and changes in the 2ndorder scaling properties has been well established. The main novelty is only the observed analytical relation (fit). I would suggest the authors to carefully revise the manuscript to clearly state this. There is a huge literature on the correction of the scaling properties due to intermittency as well as many improved cascade models have been proposed to revise the original Kolmogorov results.
 The authors claim, indeed, that the steeping of the spectrum is closely connected with intermittency. However, this could be only partially true since different spectral slopes are observed if looking along different directions with respect to the mean field. As the authors say there is a huge literature on the anisotropy of spectral slopes but they introduce a measure of the level of intermittency based on the trace of the PVI (so, something isotropic) and then also evaluate spectral slopes for the trace of the magnetic field fluctuations. Thus, my question is: how the presented results could be biased by anisotropy of magnetic field fluctuations? A possible check could be performed by looking at the dependence of the spectral slope across different directions as a function of the threshold crossing of the PVI along the different directions again. Would the results be robust or is there any dependence on the predominance of fluctuations along a specific direction?
In other words, what is the difference between an interval with PVI_{j}>2 but PVI_{k}<2 and an interval with PVI_{j}>2 for all j=x,y,z?  Another important point is that by only looking at the 2ndorder exponent could not be sufficient to fully characterize the intermittency. Indeed, as shown in literature (the authors, for example, mentioned the work by Veltri and Mangeney, 1999), intermittency is strictly related to multifractality that can only be measured by looking at the highorder scaling properties. It would be interesting to compare the intermittency magnitude with some multifractals indicators of intermittency as the multifractal width or the amplitude of the singularity spectrum (some parameters have been introduced in literature, see papers by Macek, Wawrzaszek).
 Another crucial point is the definition of the threshold above which an interval is considered intermittent, i.e., the PVI threshold. Indeed, the authors used a threshold of 2 since "The Gaussian distributions are located between the PVI range [2,2]". However, the definition of PVI is indeed a measure of the level of fluctuations with respect to an average level, i.e., something that resembles a standardization procedure. Did the authors performed the sensitivity of the results based on the choice of the threshold for identifying an intermittent interval?
Additional detailed comments
 Line 3: I would suggest to clarify that “an analytical/functional relationship…” has not been shown yet.
 Line 4: the term “intermittency magnitude” could be biased by the definition, it would be better to use the classical notation of “intermittency level”.
 Line 59: again here an analytical relation has not been shown yet, while several cascade modes have found intermittency corrections to the spectral slope.
 Lines 7475: I am not sure the whole interval from 2005 and 2013 is characterized by an undisturbed solar wind (there are different transients indeed). I would suggest to state that the selected intervals all correspond to undisturbed solar wind conditions (if this is the case).
 Line 77: please change “~” with “—“.
 Line 124: is it 15 s or 150 s as stated in line 114?
 Line 209: did you check that this is not an Alfvénic stream and then the spectrum should be f^{3/2}? If this is the case, this means that there is an intermittency correction.
 Line 232: which kind of discontinuities? This is important to understand which situation is presented.
 Line 235: could the maximum value be biased by the anisotropy of fluctuations? I mean is this really representative of something new or simply a reflection of a spectrum of anisotropic fluctuations?
 Line 244: there is a recent literature on the scaling properties and intermittency levels with Parker Solar Probe (see papers by Alberti, Cuesta, Matthaeus).

RC2: 'Comment on angeo202228', Joseph Borovsky, 20 Jan 2023
reply
This is a very interesting study, but this reader was at times confused about the methodology used in the data analysis. I am asking for a revised manuscript clarifying some of the dataanalysis methods.
 Throughout the paper, please make clear that the PSD is the magnetic PSD and that the spectral index is the magnetic spectral index.
 It seems that the plasma data is only used to get the number density in order to put the magnetic data into Alfven units. Can you clarify in the manuscript if that is true.
 There is no description in the manuscript of how the timeseries data was prepared prior to performong the FFT. Was the data windowed? Was the data interval detrended? If not, then there is an extra discontinuity in the data that adds Fourier power to the PSD. Please add a description of the timeseries preparation to the manuscript.
 The PSDs in the figures are in units of velocity, meaning that the time series of the magnetic field in Alfven units was used in the FFT. The magneticfield data has a resolution of 1/11 sec while the plasma data has a resolution of 3 sec. How were the values of the number density chosen to put the magneticfield data into Alfven units. One density value for the entire time series interval? Changing the density value every 3 seconds in the time series?.
 When putting the magnetic field into Alfven units, if one value of number density for the entire interval is not chosen, how different is the spectral index of the magnetic field in Alfven units versus the spectral index of the magnetic field in nT? I would worry that noise in the density measurements (particularly in the WIND 3sec onboard moments) would spoil the spectralindex value. Can you comment on this possibility in the manuscript.
 >42,000 intervals were examined but only 24,886 intervals were used for the statistics. That means almost half of the intervals were rejected. Besides having a higher fitting error, were there any trends to what was rejected and what was accepted?
 When the "width" of an intermittent spot is measured (line 264 and Figure 3), what are the units? Data points at 1/11sec resolution? Data points at 3sec resolution? Please clarify for the reader.
Xin Wang et al.
Xin Wang et al.
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