Anisotropic Turbulent Spectra in the Terrestrial Magnetosheath as Seen by the Cluster Spacecraft

F. Sahraoui, G. Belmont, L. Rezeau, N. Cornilleau-Wehrlin, J. L. Pinçon, and A. Balogh

Phys. Rev. Lett. 96, 075002 – Published 22 February 2006

Abstract

Here we report the first three-dimensional spatial spectrum of the low frequency magnetic turbulence obtained from the four Cluster spacecraft in the terrestrial magnetosheath close to the magnetopause. We show that the turbulence is compressible and dominated by mirror structures, its energy is injected at a large scale $k ρ \sim 0.3$ ( $l \sim 2000 km$ ) via a mirror instability well predicted by linear theory, and cascades nonlinearly and unexpectedly up to $k ρ \sim 3.5$ ( $l \sim 150 km$ ), revealing a new power law in the inertial range not predicted by any turbulence theory, and its strong anisotropy is controlled by the static magnetic field and the magnetopause normal.

Received 27 June 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.075002

Authors & Affiliations

F. Sahraoui, G. Belmont, L. Rezeau, and N. Cornilleau-Wehrlin

Centre d’Etude des Environnements Terrestre et Planétaires, IPSL, 10/12 avenue de l’Europe, 78140, Vélizy, France

J. L. Pinçon

Laboratoire de Physique et de Chimie de l’Environnement, 3A avenue de la Recherche Scientifique, 45071, Orléans, Cedex 2, France

A. Balogh

Space and Atmospheric Group, Blackett laboratory, Imperial College, Prince Consort Road, London, United Kingdom

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Vol. 96, Iss. 7 — 24 February 2006

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Images

Figure 1
The magnetic field fluctuations measured by FGM in the magnetosheath. (a) The parallel component (to $B_{0}$ ) of the magnetic fluctuations. (b) The magnitude of the whole fluctuations normalized to the mean static field $B_{0}$ . Four colors are used, one for each satellite.Reuse & Permissions
Figure 2
The temporal FFT spectra of the magnetic fluctuations, compared to the curve $f^{- 7 / 3}$ (dashed line). The vertical dotted line is the frequency corresponding to the most intense observed wave.Reuse & Permissions
Figure 3
Stationary mirror structures identified by the $k$ -filtering technique. The black curves are the isocontours of the energy density in the ( $k_{x}, k_{y}$ ) plane for four given frequencies: $f_{sc} \sim 0.3 f_{cp}$ (a), $2 f_{cp}$ (b), $3.5 f_{cp}$ (c), $4 f_{cp}$ (d). The $k$ values are normalized to the inverse proton Larmor radius ( $ρ \sim 75 km$ ). The levels 1–9 denote the lowest to highest energy values. These maxima lie almost at a constant $k_{∥}$ , $(k, B_{0}) \sim 100 °$ . The blue line is the Doppler shift $f_{sc} = k \cdot v / 2 π$ . The arrows $B_{0}$ , $n$ , and $v$ are, respectively, the directions along the local static magnetic field, the normal to the magnetopause and the flow velocity, which form here a quasiorthogonal trihedron: $(v, n) \sim 104 °$ , $(n, B_{0}) \sim 81 °$ , and $(B_{0}, v) \sim 110 °$ .Reuse & Permissions
Figure 4
The theoretical linear growth rate of the mirror instability calculated from the WHAMP program [23] for the angle $(k, B_{0}) \sim 100 °$ and using the measured parameters of the plasma. $v_{{th}_{∥}} \sim 154 km / s$ is the proton parallel thermal velocity and $ω_{cp} \sim 2.07 rd / s$ is the proton cyclotron pulsation. The vertical arrow shows the location of the wave vector ( $k ρ \sim 0.3$ ) identified at $f_{sc} \sim 0.11 Hz$ . The scales $k ρ > 0.5$ ( $γ < 0$ ) are strongly damped.Reuse & Permissions
Figure 5
A log-linear distribution of the energy density of the mirror structures identified for all the frequencies $f_{sc}$ of Fig. 2 as a function of their wave vector components (normalized to the inverse proton Larmor radius $ρ \sim 75 km$ ). The labels $∥$ , $n$ , and $v$ denote, respectively, the directions along $B_{0}$ , the magnetopause normal and the flow. The horizontal lines are the error bars.Reuse & Permissions
Figure 6
A log-log plot of the “reduced spectrum” of the magnetic energy as a function of the wave vector component $k_{v}$ along the flow $v$ direction (normalized to the inverse proton Larmor radius). It is obtained after a double integration: a temporal one over all the spacecraft frequencies of Fig. 2, providing the 3D spatial spectrum; a spatial one over the $B_{0}$ and $n$ directions. The red line is a direct fit revealing a power law $k_{v}^{- 2.6}$ . Two other power laws are plotted for comparison: $k^{- 7 / 3}$ (green) and $k^{- 5 / 3}$ (blue). The upper limit $k_{v} ρ \sim 3.5$ ( $L_{v} \sim 150 km$ ) is the smallest scale that can be measured with the 100 km Cluster separation.Reuse & Permissions

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