Testing of the Taylor Frozen-in-flow Hypothesis at Electron Scales in the Solar Wind Turbulence

Abstract

In single-spacecraft observations the Taylor frozen-in-flow hypothesis is usually used to infer wavenumber spectra of turbulence from the frequency ones. While this hypothesis can be valid at MHD scales in the solar wind because of the small phase speeds of the fluctuations in comparison with the solar wind flow speed, its validity at electron scales is questionable. In this paper, we use Cluster data to verify the validity of the Taylor hypothesis in solar wind turbulence using the test proposed in Sahraoui et al. based on the assumption that the spectral breaks occur at ρ i and ρ e . Using a model based on the dispersion relation of the linear whistler mode and the estimated ratios of the spectral breaks of the magnetic energy observed in the free-streaming solar wind, we find that 32% of the events would violate the Taylor hypothesis because of their high frequency (in the plasma rest frame) compared to the Doppler shift · (∣ ω plas / k · V ∣ > 0.5). Furthermore, the model shows that those events would correspond to whistler modes with propagation angles θ kB  ≤ 68°. The limitations of the method used and the implications of the results on future spacecraft measurements of electron-scale turbulence are discussed.