Perez & Bourouaine (Phys. Rev. Research 2, 023357, 2020) showed, using reduced-MHD simulations and phenomenological modeling, that strong incompressible MHD turbulence decorrelates in time by pure hydrodynamic sweeping: the Eulerian two-time spectrum is universal and self-similar, determined solely by the probability distribution of energy-range velocities, with a common decorrelation rate for both Elsasser fields that scales linearly with perpendicular wavenumber. The authors explicitly conjectured that this picture may be suitably extended to kinetic (non-MHD) regimes of the solar wind, but that it requires further investigation, and their closed-form results and validating simulations assume Gaussian-distributed large-scale velocities, leaving open whether the sweeping picture survives, and how it is modified, when the large-scale advecting velocities are non-Gaussian with skewed tails, as solar-wind observations show. This problem asks for the resolution of both linked questions: establish by theory, kinetic simulation (hybrid, particle-in-cell, or gyrokinetic), or multipoint spacecraft observation at ion scales whether large-scale sweeping still dominates Eulerian decorrelation and whether the self-similar, characteristic-function structure survives; and extend the sweeping model to non-Gaussian energy-range statistics with corresponding tests. A 2025 PNAS Magnetospheric Multiscale study of the collisionless magnetosheath found sweeping-consistent k^-1 decorrelation of perpendicular modes, but could not distinguish sweeping from Alfvénic propagation and did not test the universal spectrum or non-Gaussian statistics, so both cores remain open.

Background

A single spacecraft flying through the solar wind records a time series of plasma and magnetic-field fluctuations. The central statistical object for interpreting that signal is the Eulerian two-point two-time correlation — the correlation of fluctuations measured at two fixed points at two different times, with the spatial Fourier transform of the correlation defining a time-lagged spectrum S(k,τ)S(\mathbf{k},\tau). Its normalized form Γ(k,τ)=S(k,τ)/S(k,0)\Gamma(\mathbf{k},\tau)=S(\mathbf{k},\tau)/S(\mathbf{k},0), called the turbulence propagator, describes how rapidly Fourier amplitudes at wavenumber k\mathbf{k} lose memory of themselves. In incompressible magnetohydrodynamics (MHD) the turbulence is naturally described through Elsasser variables z±=u±b/4πρz^\pm=\mathbf{u}\pm\mathbf{b}/\sqrt{4\pi\rho}, the counter-propagating Alfvénic combinations of velocity and magnetic fluctuations (in velocity units, with ρ\rho the mass density).

Two mechanisms compete to set Eulerian decorrelation in strong turbulence. In the random-sweeping picture (Kraichnan, Phys. Fluids 7, 1723, 1964), small-scale eddies are passively advected by the much larger energy-containing eddies, so a fixed point decorrelates on the sweeping time τsw∼(ku0)−1\tau_{sw}\sim(ku_0)^{-1}, where u0u_0 is the rms velocity at the outer scale; the propagator is then the characteristic function (Fourier transform of the probability density) of the large-scale velocity, which is Gaussian in the time lag τ\tau when those velocities are Gaussian. Nonlinear distortion of eddies by similar-size eddies instead gives the cascade time τNL∼k−2/3\tau_{NL}\sim k^{-2/3}. In MHD a third effect appears: Alfvénic propagation along the background magnetic field at the Alfvén speed VAV_A, contributing a phase factor e∓ik∥VAτe^{\mp ik_\parallel V_A\tau} and a decorrelation time (k∥VA)−1(k_\parallel V_A)^{-1}. The measured wavenumber scaling of decorrelation times (k−1k^{-1} for sweeping versus k−2/3k^{-2/3} for straining) therefore discriminates between the mechanisms.

For the solar wind, the standard model of the inertial range is reduced MHD (RMHD) — incompressible MHD in the limit of a strong uniform guide field, describing anisotropic Alfvénic turbulence with k⊥≫k∥k_\perp\gg k_\parallel; the turbulence is balanced or imbalanced depending on whether the two Elsasser fields carry equal or unequal energies (nonzero cross helicity). Spacecraft frequency spectra are usually converted to wavenumber spectra via the Taylor frozen-in hypothesis, which assumes that temporal variations are dominated by advection of quasi-static spatial structure past the spacecraft; this assumption degrades when intrinsic decorrelation or large-scale flow fluctuations matter, so an explicit model of Eulerian time decorrelation is needed. Earlier work measured ensemble-averaged single-point two-time correlations in the solar wind (Matthaeus, Weygand & Dasso, Phys. Rev. Lett. 116, 245101, 2016), found frequency broadening consistent with a random-sweeping model (Perschke et al., Phys. Rev. Lett. 116, 125101, 2016), and found 1/k1/k propagator scaling in MHD simulations (Lugones et al., Phys. Plasmas 23, 112304, 2016). Bourouaine & Perez (ApJL 879, L16, 2019) built a phenomenological model ("BP19") of the Eulerian two-time spectrum in which decorrelation results from hydrodynamic sweeping by energy-range velocity fluctuations plus Alfvénic propagation along the local mean field.

The source paper (Perez & Bourouaine, Phys. Rev. Research 2, 023357, 2020) tested BP19 in the strong-turbulence regime against high-resolution simulations of driven RMHD turbulence, both balanced and imbalanced, and established three results: (i) both Elsasser fields z±z^\pm decorrelate at the same common rate in balanced and imbalanced turbulence; (ii) the decorrelation rate scales linearly with k⊥k_\perp with a coefficient set by the outer-scale rms velocity — pure hydrodynamic sweeping of small-scale structures by the energy-containing scales, not nonlinear straining; and (iii) the scale-dependent correlation is universal and self-similar, Γ±(k⊥,τ)=ϕv′(k⊥τ)\Gamma^\pm(k_\perp,\tau)=\phi_{v'}(k_\perp\tau), where ϕv′\phi_{v'} is the characteristic function of the probability density of the energy-range velocities, verified against the measured outer-scale velocity distribution in Gaussian-driven simulations.

The closed-form results, however, assume Gaussian-distributed outer-scale velocities (the authors note that the general propagator holds for any outer-scale velocity distribution), and the simulations use Gaussian driving, whereas solar-wind observations show that energy-containing-range fluctuations can be strongly non-Gaussian with skewed tails (Marino et al., ApJ 750, 41, 2012). The results are moreover derived strictly within incompressible MHD/RMHD, while the solar wind at and below ion scales (perpendicular wavenumbers k⊥ρi≳1k_\perp\rho_i\gtrsim1, with ρi\rho_i the ion gyroradius) is a kinetic (non-MHD) plasma in which dispersive kinetic modes (kinetic Alfvén, whistler, ion-cyclotron waves) and collisionless damping replace MHD dynamics. The authors conjecture that the universal sweeping picture "may be suitably extended to kinetic (non-MHD) regimes found in the solar wind, but it requires further investigation," and they leave decorrelation under non-Gaussian large-scale statistics unaddressed.

Problem Statement

Determine whether the sweeping-dominated, self-similar picture of the Eulerian two-time correlation established for strong incompressible (R)MHD turbulence is universal in the two specific senses not resolved by the source work, and quantify where and how it fails:

(1) Kinetic (non-MHD) regimes. Establish — by theory, by kinetic simulation (hybrid, i.e. kinetic ions plus fluid electrons; fully kinetic particle-in-cell; or gyrokinetic, a reduced kinetic description averaged over the fast ion gyromotion), or by multipoint in-situ observation at ion scales and below — whether large-scale hydrodynamic sweeping by energy-range velocity fluctuations still governs Eulerian temporal decorrelation when the small-scale dynamics are kinetic rather than MHD: whether the decorrelation rate of the Alfvénic fluctuations remains linear in k⊥k_\perp with a coefficient set by the outer-scale rms velocity and common to both counter-propagating Elsasser fields, or is instead set by kinetic decorrelation timescales (dispersive wave propagation, collisionless damping, kinetic resonances). The answer should identify the parameter regime — e.g. in terms of k⊥ρik_\perp\rho_i, the plasma beta (the ratio of thermal pressure to magnetic pressure), and cross-helicity imbalance — in which each behavior holds, and state whether the two-time spectrum in the kinetic regime remains a universal functional of the energy-range velocity statistics.

(2) Non-Gaussian large-scale statistics. Extend the sweeping model beyond the Gaussian assumption and test the extension: determine — in simulations driven with non-Gaussian, skewed energy-range velocity statistics of the kind observed in the solar wind, or in spacecraft data — whether the decorrelation still follows the characteristic function of the actual large-scale velocity distribution, and quantify the higher-cumulant corrections to that characteristic-function (sweeping) construction and the conditions under which it breaks down.

References

  1. J. C. Perez and S. Bourouaine, "Eulerian space-time correlation of strong magnetohydrodynamic turbulence", Physical Review Research 2, 023357 (2020). DOI: 10.1103/PhysRevResearch.2.023357; arXiv:2004.11458. https://doi.org/10.1103/PhysRevResearch.2.023357
  2. S. Bourouaine and J. C. Perez, "On the Interpretation of Parker Solar Probe Turbulent Signals", The Astrophysical Journal Letters 879, L16 (2019). DOI: 10.3847/2041-8213/ab288a. https://doi.org/10.3847/2041-8213/ab288a
  3. J. C. Perez, S. Bourouaine, C. H. K. Chen, and N. E. Raouafi, "Applicability of Taylor's hypothesis during Parker Solar Probe perihelia", Astronomy & Astrophysics 650, A22 (2021). DOI: 10.1051/0004-6361/202039879. https://doi.org/10.1051/0004-6361/202039879
  4. F. Pecora, W. H. Matthaeus, A. Greco, P. Dmitruk, Y. Yang, V. Carbone, and S. Servidio, "Turbulence in the terrestrial magnetosheath: Space-time correlation using the Magnetospheric Multiscale mission", Proceedings of the National Academy of Sciences 122, e2519635122 (2025). DOI: 10.1073/pnas.2519635122; arXiv:2511.15579. https://doi.org/10.1073/pnas.2519635122
  5. A. A. Azelis, J. C. Perez, and S. Bourouaine, "Space-time structure of weak magnetohydrodynamic turbulence", Journal of Plasma Physics 90, 905900109 (2024). DOI: 10.1017/S0022377824000035. https://doi.org/10.1017/S0022377824000035
  6. J. C. Perez, A. A. Azelis, and S. Bourouaine, "Two-time energy spectrum of weak magnetohydrodynamic turbulence", Physical Review Research 2, 023189 (2020). DOI: 10.1103/PhysRevResearch.2.023189. https://doi.org/10.1103/PhysRevResearch.2.023189
  7. L. Zhao, G. P. Zank, and H. Li, "Non-propagating structures and propagating waves in solar wind turbulence revealed by simulations and observations", Reviews of Modern Plasma Physics 9, 24 (2025). DOI: 10.1007/s41614-025-00200-y. https://doi.org/10.1007/s41614-025-00200-y
  8. S. Bourouaine and J. C. Perez, "Interpreting Solar Wind Turbulent Spectra beyond Taylor's Hypothesis", The Astrophysical Journal Letters 893, L32 (2020). DOI: 10.3847/2041-8213/ab7fb1. https://doi.org/10.3847/2041-8213/ab7fb1
  9. R. Marino, L. Sorriso-Valvo, R. D'Amicis, V. Carbone, R. Bruno, and P. Veltri, "On the occurrence of the third-order scaling in high latitude solar wind", The Astrophysical Journal 750, 41 (2012). DOI: 10.1088/0004-637X/750/1/41. https://doi.org/10.1088/0004-637X/750/1/41
  10. W. H. Matthaeus, J. M. Weygand, and S. Dasso, "Ensemble space-time correlation of plasma turbulence in the solar wind", Physical Review Letters 116, 245101 (2016). DOI: 10.1103/PhysRevLett.116.245101. https://doi.org/10.1103/PhysRevLett.116.245101
  11. C. Perschke, Y. Narita, U. Motschmann, and K.-H. Glassmeier, "Observational Test for a Random Sweeping Model in Solar Wind Turbulence", Physical Review Letters 116, 125101 (2016). DOI: 10.1103/PhysRevLett.116.125101. https://doi.org/10.1103/PhysRevLett.116.125101
  12. R. Lugones, P. Dmitruk, P. D. Mininni, M. Wan, and W. H. Matthaeus, "On the spatio-temporal behavior of magnetohydrodynamic turbulence in a magnetized plasma", Physics of Plasmas 23, 112304 (2016). DOI: 10.1063/1.4968236. https://doi.org/10.1063/1.4968236
  13. Y. Nariyuki, "Anomalous diffusion model in Fourier space describing time correlation of shear Alfvénic turbulence", Physics of Plasmas 31, 122303 (2024). DOI: 10.1063/5.0220185. https://doi.org/10.1063/5.0220185
  14. J. C. Palacios, S. Bourouaine, and J. C. Perez, "On the Statistics of Elsasser Increments in Solar Wind and Magnetohydrodynamic Turbulence", The Astrophysical Journal Letters 940, L20 (2022). DOI: 10.3847/2041-8213/ac92f6. https://doi.org/10.3847/2041-8213/ac92f6
  15. R. H. Kraichnan, "Kolmogorov's Hypotheses and Eulerian Turbulence Theory", The Physics of Fluids 7, 1723-1734 (1964). DOI: 10.1063/1.2746572. https://doi.org/10.1063/1.2746572