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

S Y Huang,F Sahraoui

doi:10.3847/1538-4357/ab17d3

Abstract

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.

Highlights

In the solar wind, high-time-resolution electric and magnetic field observations from different spacecraft such as Stereo, Cluster, and THEMIS provide good opportunities to investigate turbulence cascades from magnetohydrodynamic (MHD) scales down to electron scales (e.g., Kiyani et al 2009, 2015, Sahraoui et al 2009, 2010a; 2013, Alexandrova et al 2012; Salem et al 2012; Chen et al 2013)
The Taylor hypothesis is usually used in the solar wind turbulence to infer wavenumber spectra from frequency spectra because the characteristic phase speeds in the solar wind (VA ∼ Cs < 100 km s−1) are much flow velocity
Than the plasma as the turbulence cascade approaches the electron scale, dispersive modes with phase speeds comparable to or larger than the flow speed may exist, which makes the validity of the Taylor hypothesis questionable

Summary

Introduction

High-time-resolution electric and magnetic field observations from different spacecraft such as Stereo, Cluster, and THEMIS provide good opportunities to investigate turbulence cascades from magnetohydrodynamic (MHD) scales down to electron scales (e.g., Kiyani et al 2009, 2015, Sahraoui et al 2009, 2010a; 2013, Alexandrova et al 2012; Salem et al 2012; Chen et al 2013). Due to the supersonic and super-Alfvénic nature of the solar wind, the Taylor hypothesis is often used to derive wavenumber spectra along the plasma flow direction from the observed ones in the spacecraft frame (ωplas = k·V ωsc ∼ k·V = kV cosθkV) While this assumption is likely to be valid at MHD scales, it may totally fail at electron scales where dispersive modes that have phase speeds comparable or higher than the flow speed Vf may exist, e.g., the quasi-parallel whistler (Lacombe et al 2014). At those scales only stationary structures or very-low-frequency fluctuations such as high oblique kinetic Alfvén waves (KAWs) can fulfill the Taylor hypothesis (e.g., Saito et al 2010; Sahraoui et al.2012; Howes et al 2014; Zhao et al 2014; Chen & Boldyrev 2017)

Methods

Results

Discussion

Conclusion