Fraction of Energy Carried by Coherent Structures in the Turbulent Cascade in the Solar Wind.

(Solar Orbiter Nugget #87 A. Bendt^1,2 and S. Chapman²)

Introduction

The solar wind is known to exhibit intervals of turbulence. Turbulence is a potential mechanism to heat the solar wind [1]. Fluctuations due to solar wind turbulence exhibits three distinct ranges in their power spectrum, at large scales the so-called 1/f range, at intermediate scales the inertial range, and at small scales the kinetic range. Recently, an additional spectral break has been found dividing the inertial range into two subranges (e.g. [2]). Coherent structures, such as for example current sheets, reconnection, switchbacks, and flux ropes, have been identified in solar wind turbulence [3]. They have further been identified as sites of enhanced proton temperatures and thus may drive heating of the solar wind (e.g. [4]). Coherent structures are identified here, by the presence of sharp gradients that can drive dissipative heating. We use Solar Orbiter magnetic field observations of solar wind turbulence from 0.3 au - 1 au to determine the fraction of power that is carried by coherent structures.

Methods

We use the method first proposed by Bendt & Chapman 2025 [5] to identify coherent structures, illustrated in Fig. 1 a and b. This method is based on a comparison of the distributions of the partial variance increment obtained from two different wavelet decompositions, using the Haar and 10th-order Daubechies (Db10) wavelets, which are sensitive to wave-packets and discontinuities respectively (Fig.1a). The partial variance increment using the fluctuations obtained from wavelet decompositions is equivalent to the square-root local intermittency measure. We compare the distributions (Fig. 1a), scale-by-scale, using compensated Quantile-Quantile plots (QQ-plots) (Fig. 1b). Following this method, we obtain a threshold above which fluctuations may be coherent structures (Fig. 1b). This threshold denotes the value above which fluctuations may be coherent structures. We then compute the percentage of the total power in magnetic field fluctuations that is above this threshold (Fig. 1c). We compare this percentage of the total power in coherent structures  (LIM-P(f_n)) across the inertial and kinetic ranges and across heliocentric distances.

Figure 1. Illustration of the method used to obtain estimates of the power in coherent structures. Panels (a) and (b) (from [5]) show the method first proposed therein to identify the coherent structure threshold. Panel (a) shows examples of the square-root local intermittency measure probability density functions (pdfs) of Haar (red) and Db10 (blue) wavelet decompositions of the magnetic field component B_⟂(BxVsw)  of one solar wind interval. The decompositions shown are performed at 0.25 s timescale. Panel (b) shows the compensated QQ plots for the same interval shown in panel (a); these compare the square-root local intermittency measure pdfs obtained from the two wavelet decompositions performed at all temporal kinetic range scales (lighter colours denote longer temporal scales). The black vertical line and grey shading indicate the average threshold and its variance, respectively. Panel (c) shows the percentage of the power LIM-P(f_n) in fluctuations above the threshold versus frequency f_n for the same magnetic field component as in panels (a,b) for all intervals at <0.4 au.

Results

Figure 2 (top row) presents the percentage of total power that is carried by coherent structures (LIM-P(f_n)) for all intervals, divided into three categories based on heliocentric distance, across the inertial and kinetic ranges obtained for the magnetic field component B_⟂(BxVsw). The bottom row of Fig. 2 presents the power spectral densities of the total magnetic field component and of the power carried by coherent structures of one example interval within each category. 

We find that the percentage of the total power associated with coherent structures is significant, maximising at ~50% just below the frequency of transition between the inertial and kinetic ranges. In the inertial range within 0.4 au, the percentage of power in coherent structures increases roughly linearly with increasing frequency (Fig.2 a). Beyond 0.4 au (Fig.2 b and c), we identify two subranges in the inertial range in the percentage of power in coherent structures. In the kinetic range, the percentage of power in coherent structures decreases approximately linearly with increasing frequency (Fig.2 a-c).

Figure 2. Power in coherent structures as a function of frequency. Results are plotted for the magnetic field component B_⟂(BxVsw). Left to right, the panels group the intervals by heliocentric distance: panels (a), (d) R <  0.4 au; panels (b), (e) 0.4 ≤ R < 0.8 au; and panels (c), (f) R ≥ 0.8 au. Upper panels plot the percentage of power in coherent structures LIM-P(f_n) and lower panels overplot the power spectral density of coherent structures (purple ×, grey shading) on the total power (purple) for one of these intervals. On all panels, black vertical lines denote the 1 hr, 1 minute, and 1 s timescales. On upper panels, the vertical grey shading indicates the range of frequencies of the ion-gyro radius of all intervals. The ion-gyro radius in the lower panels is indicated by a black vertical line. In the upper panels, the colours denote plasma beta, β < 0.5 (blue), 0.5 ≤ β < 2 (red), and β≥2 (black). Field-alignment angle value (range 0°–90° obtained by folding in angles ≥90°): θ < 20° (+), 20°–60° (∘), and θ ≥ 60° (△).

Conclusions

Our result of a significant percentage of the total power being carried by coherent structures provides quantitative support for the idea that coherent structures are important for solar wind heating. The trend of the percentage of power in coherent structures suggests that in the inertial range wave-wave interactions at larger scales are systematically supplanted by coherent structures at smaller scales. The percentage of power in coherent structures exhibiting two subranges in the inertial range provides the first physical insight into the recently discovered subranges in the inertial range.

This nugget is based on the following paper: Bendt&Chapman, ApJL, 998 L2 (2026)

Affiliations

(1) SERENE, School of Engineering, University of Birmingham, Birmingham B15 2TT, United Kingdom
(2) Centre for Fusion, Space and Astrophysics, Physics Department, University of Warwick, Warwick CV4 7AL, United Kingdom

References

[1] Marino, R., Sorriso-Valvo, L., Carbone, V., et al. 2008, ApJL, 677, L71, https://dx.doi.org/10.1086/587957
[2] Wicks, R. T., Horbury, T. S., Chen, C. H. K., & Schekochihin, A. A. 2011, Phys. Rev. Lett., 106, 045001, https://link.aps.org/doi/10.1103/PhysRevLett.106.045001
[3] Hnat, B., Chapman, S., & Watkins, N. 2021, Phys. Rev. Lett., 126, 125101, https://link.aps.org/doi/10.1103/PhysRevLett.126.125101
[4] Osman, K. T., Matthaeus, W. H., Wan, M., & Rappazzo, A. F. 2012, Phys. Rev. Lett., 108, 261102, https://link.aps.org/doi/10.1103/PhysRevLett.108.261102
[5] Bendt, A., & Chapman, S. C. 2025, Phys. Rev. Res., 7, 023176, https://link.aps.org/doi/10.1103/PhysRevResearch.7.023176