Turbulence in the terrestrial magnetosheath: space-time correlation using the Magnetospheric Multiscale mission

Abstract

Spatiotemporal correlation of magnetic field fluctuations is investigated using the Magnetospheric Multiscale mission in the terrestrial magnetosheath. The first observation of the turbulence propagator in space emerges through analysis of more than a thousand intervals. Results show clear features of spatial and spectral anisotropy, leading to a distinct behavior of relaxation times in the directions parallel and perpendicular to the mean magnetic field. Full space-time investigation of the Taylor hypothesis reveals a scale-dependent anisotropy of magnetosheath fluctuations that can be compared to the effect of flow propagation on spacecraft frame time decorrelation rates as well as with Eulerian estimates. The turbulence propagator reveals that the amplitudes of the perpendicular modes decorrelate according to sweeping or Alfvénic propagation mechanisms. The decorrelation time of parallel modes instead does not depend on the parallel wavenumber, which could be due to resonant interactions. Through direct observation, this study provides unprecedented insight into the space-time structure of turbulent space plasmas, while giving critical constraints for theoretical and numerical models.

Figures (8)

• Figure 1: Space-time correlation function with complete coverage of the space-time domain. The red oblique line is the direction along a plasma parcel flowing at a speed of $100$ km/s.
• Figure 2: 1D cuts of the normalized two-point two-time correlation function. The sample along a nominal 100 km/s flow speed is the red line with "+" symbols. The purely spatial (vertical) direction $\tau=0$ is the green line with "x" symbols. The purely temporal (Eulerian, horizontal) sampling at $r=0$ is the blue line with circles. The horizontal line at $1/e$ marks where correlation times and lengths are estimated (annotated in the figure and reported in Table \ref{['tab:table1']}).
• Figure 3: Decorrelator in the (a) $(k_\parallel,\tau)$ and (b) $(k_\perp,\tau)$ planes. (c), (d) Horizontal cuts of the decorrelator in the wavenumber range $1.3 \times 10^{-3}~\mathrm{km^{-1}} < k < 4.5 \times 10^{-3}~\mathrm{km^{-1}}$ for $k_\parallel$ and $k_\perp$ respectively. For each wavenumber, the correlation time is determined by the intercept with the $1/e$ horizontal line. For clarity, the lines are trimmed below the $1/e$ threshold. The labels report a few $k$ values to guide the reader through colors. $k$ is in units of $10^{-3}$ km$^{-1}$.
• Figure 4: Scale-dependent time decorrelation of parallel and perpendicular wavenumbers. Blue "x" and red "+" symbols are the $1/e$-intercepts of $\Gamma$ profiles in Fig. \ref{['fig:Skt']} for $k_\parallel$ and $k_\perp$ respectively. Reported are reference scalings for the nonlinear strain ($k^{-2/3}$ dashed line) and sweeping ($k^{-1}$ dotted line) predictions. Parallel decorrelation times do not show dependence on the parallel wavenumber, suggesting independent decorrelation mechanisms. Perpendicular decorrelation times are fitted with a power law (dash-dotted line) providing a scaling exponent of $-0.98 \pm 0.02$ in excellent agreement with sweeping or Alfvénic theoretical predictions.
• Figure 5: Position of the 1180 MMS magnetosheath intervals (green symbols). Nominal magnetopause boundary indicated with a thick black line. Earth is depicted as a blue circle. The inset shows the MMS constellation on 2018 Feb 17, 22:08:43, corresponding to the interval highlighted with a red symbol. The units of position in the inset are in km relative to the position of the barycenter.