Spectra and anisotropy of magnetic fluctuations in the Earth's   magnetosheath: Cluster observations
  We investigate the spectral shape, the anisotropy of the wave vector distributions and the anisotropy of the amplitudes of the magnetic fluctuations in the Earth's magnetosheath within a broad range of frequencies. We present the first observations of a Kolmogorov-like inertial range of Alfvenic fluctuations in the magnetosheath flanks, below fci. In the vicinity of fci, a spectral break is observed, like in solar wind turbulence. Above the break, the energy of compressive and Alfvenic fluctuations generally follow a power law with a spectral index between -3 and -2. Concerning the anisotropy of the wave vector distribution, we observe a change in its nature in the vicinity of ion characteristic scales: if at MHD scales there is no evidence for a dominance of a slab (k||>kperp) or 2D (kperp>k||) turbulence, above the spectral break, (f>fci, kc/wpi>1) the 2D turbulence dominates. This 2D turbulence is observed in six selected one-hour intervals among which the average proton beta varies from 0.8 to 9. It is observed for both the transverse and compressive magnetic fluctuations, independently on the presence of linearly unstable modes at low frequencies or Alfven vortices at the spectral break. We then analyse the anisotropy of the magnetic fluctuations in a time dependent reference frame based on the field B and the flow velocity V directions. Within the range of the 2D turbulence, at scales [1,30]kc/wpi, and for any beta we find that the magnetic fluctuations at a given frequency in the plane perpendicular to B have more energy along the BxV direction. This non-gyrotropy of the fluctuations is consistent with gyrotropic fluctuations at a given wave vector, with kperp>k||, which suffer a different Doppler shift along and perpendicular to V in the plane perpendicular to B. 
Olga Alexandrova, Catherine Lacombe, Andre Mangeney