Turbulence in the solar wind: 3D measurements of wavenumber spectra using the k-filtering technique

Magnetic turbulence in the solar wind has been studied for many years. Most of the observational work have been -5/3 focused on the large (MHD) scales, i.e. the so-called inertial range with a Kolmogorov scaling k^-5/3 [e.g.,1,2]. The inertial range is widely believed to form by strong nonlinear interaction of Alfvén waves. However, the anisotropy of the turbulence (in wavenumber space) is still hotly debated [e.g., 3]. From single spacecraft data, inferring the wavenumber spectra from the temporal measured ones onboard the satellite can be achieved only by using the Taylor frozen-in assumption ω_sat~k.V_sw. This means that all the phase speeds of the waves need to be smaller than the solar wind speed V_sw. While this assumption is generally valid at MHD scales (because the Alfvén speed V_A <;<;V_sw), it breaks down at the sub-ion (and electron) scales where whistler modes may exit. Moreover, even when the Taylor assumption is justified it can yield only one component of the wavenumber spectra: along the flow V_sw [4-6]. The two other directions perpendicular to V_sw are thus missing unless additional assumptions, such as isotropy, are used. Therefore multispacraft data and appropriate space-correlations methods are necessary in order to fully determine the 3D wavenumber spectra of space turbulence. This can be achieved by applying the k-filtering technique on the four Cluster spacecraft data.