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 [ 10 ^ { -3 } , 10 ] Hz which corresponds to spatial scales from \sim 10 to 10 ^ { 5 } km .
We present the first observations of a Kolmogorov-like inertial range of Alfvénic fluctuations \delta B ^ { 2 } _ { \perp } \sim f ^ { -5 / 3 } in the magnetosheath flanks , below the ion cyclotron frequency f _ { ci } .
In the vicinity of f _ { ci } , a spectral break is observed , like in solar wind turbulence .
Above the break , the energy of compressive and Alfvénic 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 clear 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 _ { \| } \gg k _ { \perp } ) or 2D ( k _ { \perp } \gg k _ { \| } ) turbulence , above the spectral break , ( f > f _ { ci } , kc / \omega _ { pi } > 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 Alfvén vortices at the spectral break .
We then analyse the anisotropy of the magnetic fluctuations in a time dependent reference frame based on the field { \bf B } and the flow velocity { \bf V } directions .
Within the range of the 2D turbulence , at scales [ 1 , 30 ] kc / \omega _ { pi } , and for any \beta we find that the magnetic fluctuations at a given frequency in the plane perpendicular to { \bf B } have more energy along the { \bf B } \times { \bf V } direction .
This non-gyrotropy of the fluctuations at a fixed frequency is consistent with gyrotropic fluctuations at a given wave vector , with k _ { \perp } \gg k _ { \| } , which suffer a different Doppler shift along and perpendicular to { \bf V } in the plane perpendicular to { \bf B } .