On the Limitation of Taylor’s Hypothesis in Parker Solar Probe’s Measurements near the Alfvén Critical Point

In this Letter, we present an analysis of two-point, two-time correlation functions from high-resolution numerical simulations of Reflection-driven Alfvén Turbulence near the Alfvén critical point r c. The simulations model the turbulence in a prescribed background solar wind model chosen to match observational constraints. This analysis allows us to investigate the temporal decorrelation of solar wind turbulence and the validity of Taylor’s approximation near the heliocentric distance r c, which Parker Solar Probe (PSP) is expected to explore in the coming years. The simulations show that the temporal decay of the Fourier-transformed turbulence decorrelation function is better described by a Gaussian model rather than a pure exponential time decay, and that the decorrelation frequency is almost linear with perpendicular wave number k ⊥ (perpendicular with respect to the background magnetic field \({{\boldsymbol{B}}}_{0}\)). Based on the simulations, we conclude that Taylor’s approximation cannot be used in this instance to provide a connection between the frequency ω of the time signal (measured in the probe frame) and the wavevector k ⊥ of the fluctuations because the frequency k ⊥ V sc (V sc is the spacecraft speed) near r c is comparable to the estimated decorrelation frequency. However, the use of Taylor’s approximation still leads to the correct spectral indices of the power spectra measured at the spacecraft frame. In this Letter, based on a Gaussian model, we suggest a modified relationship between ω and k ⊥, which might be useful in the interpretation of future PSP measurements.