Non-universality of the Turbulent Spectra at Sub-ion Scales in the Solar Wind: Dispersive Effects versus the Doppler Shift

Large surveys of the power spectral density of the magnetic fluctuations in the solar wind have reported different slope distributions at MHD, sub-ion and sub-electron scales: the smaller the scale, the broader the distribution. Here, we review briefly some of the most relevant explanations of the broadening of the slopes at sub-ion scales. Then, we present a new one that has been overlooked in the literature, which is based on the relative importance of the dispersive effects with respect to the Doppler shift due to the mean flow speed. We build a toy model based on a dispersion relation of a linear mode that matches at high frequency ( ω ≳ ω _ci ) the Alfvén (respectively whistler) mode at high oblique (respectively quasi-parallel) propagation angles θ _kB . Starting with a double power-law spectrum of turbulence ${{k}_{\perp }}^{-1.66}$ in the inertial range and ${{k}_{\perp }}^{-2.8}$ at the sub-ion scales, the transformed spectrum (in frequency f ) as it would be measured in the spacecraft reference frame shows a broad range of slopes at the sub-ion scales that depend both on the angle θ _kB and the flow speed V . Varying θ _kB in the range 4°–106° and V in the range 400−800 km s ^−1 the resulting distribution of slopes at the sub-ion scales reproduces quite well the observed one in the solar wind. Fluctuations in the solar wind speed and the wavevector anisotropy of the turbulence may explain (or at least contribute to) the variability of the spectral slopes reported from spacecraft observations in the solar wind