On the Interpretation of Parker Solar Probe Turbulent Signals

Abstract

In this letter we propose a practical methodology to interpret future Parker Solar Probe (PSP) turbulent time signals even when Taylor's hypothesis is not valid. By extending Kraichnan's sweeping model used in hydrodynamics we derive the Eulerian spacetime correlation function in magnetohydrodynamics (MHD) turbulence. It is shown that in MHD, the temporal decorrelation of small-scale fluctuations arises from a combination of hydrodynamic sweeping induced by large-scale fluid velocity δ u 0 and by the Alfvénic propagation along the local magnetic field. The resulting temporal part of the space-time correlation function is used to determine the wavenumber range ∆k ⊥ = [k min , k max ] of the turbulent fluctuations that contribute to the power of a given frequency ω of the time signal measured in the spacecraft frame. Our analysis also shows that the shape of frequency power spectrum P sc (ω) of the time signal will follow the same power-law of the reduced power spectrum E(k ⊥ ) ∼ k −α ⊥ in the plasma frame, where α is the spectral index. The proposed framework for the analysis of PSP time signals entirely relies on two simple dimensionless parameters that can be empirically obtained from PSP measurements, namely, ε = δ u 0 / √ 2V ⊥ (where V ⊥ is the perpendicular velocity of PSP seen in the plasma frame) and the spectral index α.

The near-Sun streamer belt solar wind: turbulence and solar wind acceleration

“…Figure 2 also contains the time series of the parameter = δv rms / √ 2v sc calculated from 1-hour intervals, where v sc is the magnitude of the solar wind velocity in the spacecraft frame. This is the same parameter as in the model of Bourouaine & Perez (2019), in which perpendicular sampling is assumed so v sc ∼ v sc⊥ , and in which the Taylor hypothesis is valid for 1. The model also assumes Gaussian random sweeping and anisotropic turbulence k ⊥ k , and it is valid when tan(θ BV ) δv rms /v A , where θ BV is the angle between B 0 and the mean solar wind velocity in the spacecraft frame.…”

Turbulence Characteristics of Switchback and Nonswitchback Intervals Observed by Parker Solar Probe

“…To estimate the corresponding perpendicular correlation lengths from the obtained correlation times we invoke Taylor's Hypothesis. Although the ratio V A /V ⊥ ∼1 (where V ⊥ is the perpendicular velocity of the spacecraft seen in the plasma frame), Bourouaine & Perez (2019, showed that Taylor approximation can still be valid if the dimensionless parameter…”

The Radial Dependence of Proton-scale Magnetic Spectral Break in Slow Solar Wind during PSP Encounter 2

“…Due to the comparable Alfvén and solar wind, and spacecraft speeds, it is unclear whether the Taylor hypothesis is valid for PSP observations during its perihelion (Narita et al 2013;Bourouaine & Perez 2018Chhiber et al 2019). Recent work from Chaspis (2020, to be submitted) suggests the Taylor hypothesis may not be applicable when PSP is below 40 solar radii (0.19 AU).…”