Observational adjudication of the dynamical origin of Eulerian (plasma-frame) decorrelation in solar wind turbulence

Multi-spacecraft measurements show that the plasma-frame (Eulerian) decorrelation of solar wind magnetic turbulence differs sharply between slow, quasi-two-dimensional wind ($T_c=215\pm43$ min) and fast, slab-dominated wind ($T_c=114\pm23$ min), yet the physical mechanism producing these times is not identified: when Weygand, Matthaeus, Kivelson and Dasso (2013) compared them with the six then-available Eulerian-correlation models (magnetostatic; undamped shear Alfvén waves; the damping model of dynamical turbulence; random sweeping; and two nonlinear Alfvénic decay time variants), none reproduced the data, all fell within about a factor of three, and the predictions proved highly sensitive to poorly constrained inputs (the correlation length $L_c$, the scale ratio $L_{\parallel}/L_{\perp}$, the dynamical parameter $\alpha$, and the spectral form). Direct numerical simulations and the Bourouaine-Perez phenomenology establish sweeping by energy-containing-scale velocities plus Alfvénic propagation as the expected inertial-range mechanism, and a 2025 Magnetospheric Multiscale study observed this mechanism competition directly in the magnetosheath; however, no work has performed the corresponding observational adjudication in the solar wind itself with independently constrained parameters, scale-resolved decorrelation, or joint magnetic-velocity analysis. The problem, which is a stated objective of the HelioSwarm constellation mission, remains open.

Background

Near-Earth space plasmas are observed mostly by single spacecraft moving with the solar wind, so a measured time series conflates spatial structure with intrinsic temporal evolution. The standard remedy is the Taylor frozen-in flow hypothesis, which assumes turbulent structures are advected past the spacecraft much faster than they evolve, so that time lags map directly onto spatial separations. The intrinsic, plasma-frame temporal evolution is described by the Eulerian correlation function $E(t)$, the autocorrelation of the fluctuations at a fixed point moving with the mean flow, whose characteristic scale is the '1/e' decorrelation time $T_c$, the lag at which the normalized correlation falls to $1/e$. $E(t)$ matters beyond turbulence theory itself: its Fourier transform (the plasma-frame Eulerian frequency spectrum) controls resonant scattering of charged particles, for example near 90-degree pitch angles, and decorrelation times enter explicit theories of perpendicular diffusion and magnetic field-line random walk.

Direct measurement of $E(t)$ requires separating spatial from temporal decorrelation. Building on Matthaeus, Dasso, Weygand, Kivelson and Osman (2010), Weygand, Matthaeus, Kivelson and Dasso (2013) used simultaneous magnetic-field measurements from seven spacecraft (ACE, Wind, Geotail, IMP-8, Interball and the THEMIS/ARTEMIS P1 and P2 probes) to estimate the Eulerian correlation as the ratio of a single-spacecraft time-lagged correlation, evaluated at the transit time between a spacecraft pair, to the simultaneous two-point correlation of that pair. They obtained $T_c=226\pm18$ min over all speeds, $215\pm43$ min in the slow wind (below about 450 km/s), where quasi-two-dimensional turbulence (fluctuations with wavevectors nearly perpendicular to the mean magnetic field) dominates, and $114\pm23$ min in the fast wind (above about 600 km/s), where slab-type turbulence (wavevectors nearly parallel to the mean field) dominates.

The unresolved issue is which physical mechanism sets these times. The comparison set is the family of theoretical Eulerian-correlation models compiled by Shalchi (2008): (i) magnetostatic turbulence, with no intrinsic time evolution; (ii) undamped shear Alfvén waves, with a decorrelation time $L_{slab}/V_A$, where $V_A$ is the Alfvén speed associated with the mean field; (iii) the damping model of dynamical turbulence, in which resonant wave damping shortens the wave lifetime, with timescale $L_{slab}/(\alpha V_A)$; (iv) the random sweeping model, in which inertial-range fluctuations are advected past a fixed point by the large, energy-containing-scale flow and decorrelate on a time of order $1/(k_\perp Z)$, where $k_\perp$ is the fluctuation wavenumber perpendicular to the mean magnetic field and $Z$ is the total turbulence amplitude in speed units (Chen and Kraichnan, 1989); and (v)-(vi) two variants of the nonlinear Alfvénic decay time (NADT) model, in which decorrelation proceeds through nonlinear interactions between counterpropagating Alfvénic fluctuations, one dominated by plasma-wave effects ($L_{slab}/V_A$) and one by dynamical-turbulence effects, with timescale $(1/\sqrt2)(B_0/\Delta B_{2d})(L_{2d}/V_A)$, where $B_0$ is the mean magnetic field magnitude and $\Delta B_{2d}$ and $L_{2d}$ are the fluctuation amplitude and correlation scale of the quasi-two-dimensional component. The dynamical parameter $\alpha$, ranging from 0 to 1, interpolates between magnetostatic ($\alpha=0$) and strongly dynamical ($\alpha=1$) turbulence.

Using nominal near-Earth inputs (correlation lengths $L_c$ of roughly $1.3$-$1.7\times10^6$ km, mean field 5 nT, fluctuation amplitude 1 nT, Alfvén speeds of 85 km/s in fast and 58 km/s in slow wind), Weygand et al. found that none of these models reproduces the measured times, although all fall within about a factor of three. The comparison is degenerate because the predicted times are extremely sensitive to inputs that are themselves poorly constrained: the correlation length $L_c$, the ratio $L_{\parallel}/L_{\perp}$ of parallel to perpendicular correlation lengths (the model compilation assumed $L_{\parallel}=10L_{\perp}$, whereas multi-spacecraft observations indicate $L_{\parallel}\approx2L_{\perp}$), the dynamical parameter $\alpha$, and the assumed form of the energy spectrum. Because the measured 1/e time weights the large energy-containing scales heavily, even an elementary two-component estimate, in which the decorrelation time is the energy-weighted average of the large-eddy turnover time $T_0=L/Z$ and the faster inertial-range time, already matches the data without discriminating among mechanisms at small scales. Direct numerical simulations of magnetohydrodynamic turbulence (Servidio, Carbone, Dmitruk and Matthaeus, 2011) indicate that random sweeping dominates inertial-range decorrelation. More recent theory (Bourouaine and Perez, 2019; Perez and Bourouaine, 2020) derives an Eulerian space-time correlation in which small-scale decorrelation combines hydrodynamic sweeping by energy-containing-range velocities with Alfvénic propagation along the local mean field, validated against direct numerical simulations of reduced magnetohydrodynamics (an approximation retaining Alfvénic fluctuations propagating along a strong mean magnetic field); this modern model has not yet been tested against plasma-frame multi-point correlations in the solar wind, and the older model family remains in routine use in charged-particle transport theory.

Problem Statement

Determine, observationally and with controlled parameters, the physical mechanism and quantitative model of plasma-frame (Eulerian) temporal decorrelation of near-Earth solar wind turbulence. Concretely: (1) adjudicate among the candidate dynamical-turbulence models for the Eulerian correlation function $E(t)$, namely the undamped shear Alfvén wave, the damping model of dynamical turbulence, random sweeping, and the nonlinear Alfvénic decay time (NADT) variants drawn from the six-model comparison set compiled by Shalchi (2008) (the sixth, magnetostatic, model has no intrinsic time evolution and cannot produce a finite $T_c$, so it is excluded a priori), together with successors such as the Bourouaine-Perez sweeping-plus-Alfvénic-propagation model, using speed-resolved multi-point measurements in both the slow (quasi-two-dimensional-dominated) and fast (slab-dominated) solar wind, with the governing inputs (correlation length $L_c$, scale ratio $L_{\parallel}/L_{\perp}$, dynamical parameter $\alpha$, spectral form) constrained independently of the decorrelation data being explained; (2) quantify the relative contributions of energy-containing-range and inertial-range scales to the measured decorrelation, that is, whether the observed 1/e time is set by the large-eddy turnover time or by faster sweeping or wave processes, through scale-resolved decorrelation estimates rather than a single fitted exponential; and (3) incorporate co-temporal velocity (plasma) measurements, or rigorously bound their effect, so that the joint magnetic-velocity decorrelation is characterized rather than the magnetic field alone. These three components jointly serve one objective, namely a validated account of the operative decorrelation physics: the model comparison is meaningless without independently constrained parameters, and incomplete without the scale decomposition and plasma data. The problem is solved when a quantitative account reports, at a stated statistical significance, which of the adjudicated model families the observations exclude and which remain viable, and reproduces the measured wind-speed dependence (decorrelation times of $215\pm43$ min in slow wind versus $114\pm23$ min in fast wind) from independently constrained inputs. The source paper additionally defers the downstream consequences of speed-dependent decorrelation for charged-particle scattering, perpendicular diffusion, field-line random walk, and solar-cycle modulation of galactic cosmic rays to dedicated studies; such transport modeling is a natural application of, but not a substitute for, the adjudication requested here.

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