Abstract
We investigate the validity of Taylor’s hypothesis (TH) in the analysis of velocity and magnetic field fluctuations in Alfvénic solar wind streams measured by Parker Solar Probe (PSP) during the first four encounters. The analysis is based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence, which has been validated in high-resolution numerical simulations of strong reduced MHD turbulence. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameterϵ = δu0/√2V⊥, which quantifies the ratio between the typical speed of large-scale fluctuations,δu0, and the local perpendicular PSP speed in the solar wind frame,V⊥. TH is expected to be applicable forϵ≲ 0.5 when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfvén Mach numberMA=VSW∕VA, whereVSWandVAare the local solar wind and Alfvén speed, respectively. For the four selected solar wind intervals, we find that between 10 and 60% of the time, the parameterϵis below 0.2 and the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than 30°. For angles above 30°, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrumE(k⊥) of magnetic fluctuations from its measured frequency spectra. The spectral indices determined from power-law fits of the measured frequency spectrum accurately represent the spectral indices associated with the underlying spatial spectrum of turbulent fluctuations in the plasma frame. Aside from a frequency broadening due to large-scale sweeping that requires careful consideration, the spatial spectrum can be recovered to obtain the distribution of fluctuation’s energy across scales in the plasma frame.
Highlights
The analysis of spacecraft signals invariably requires a number of assumptions to properly interpret temporal variations in terms of their corresponding spacetime variations in the plasma frame of reference, defined as the frame where the mean plasma bulk velocity is zero
The average spacecraft speed measured in the plasma frame ranges from 300 to nearly 500 km s−1, so that the interval selection covers both slow and fast solar wind streams
We have presented an analysis of four 24 h intervals during the first four Parker Solar Probe (PSP) close encounters to investigate the applicability of Taylor’s hypothesis (TH) in the framework of a recent methodology (Bourouaine & Perez 2019, 2020)
Summary
The analysis of spacecraft signals invariably requires a number of assumptions to properly interpret temporal variations in terms of their corresponding spacetime variations in the plasma frame of reference, defined as the frame where the mean plasma bulk velocity is zero. Bourouaine & Perez (2019, hereafter BP19), propose a new methodology to interpret turbulent signals beyond TH based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence, which was validated for strong MHD turbulence in high-resolution numerical simulations of reduced MHD (RMHD) turbulence (Perez & Bourouaine 2020) This new methodology, which assumes that the turbulence is Alfvénic and highly anisotropic (k /k⊥ 1 where k and k⊥ are the parallel and perpendicular components of the wavevector with respect to the magnetic√field), depends on a single dimensionless parameter = δu0/ 2V⊥, where δu0 is the rms value of the outer-scale fluid velocity (above the onset of the inertial range) and V⊥ is the field-perpendicular velocity of the spacecraft in the plasma frame.
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