On the interpretation of Parker Solar Probe Turbulent Signals

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 $\delta u_0$ and by the Alfv\'enic propagation along the local magnetic field. The resulting temporal part of the space-time correlation function is used to determine the wavenumber range $\Delta k_\perp=[k_{\rm min},k_{\rm max}]$ of the turbulent fluctuations that contribute to the power of a given frequency $\omega$ of the time signal measured in the spacecraft frame. Our analysis also shows that the shape of frequency power spectrum $P_{sc}(\omega)$ of the time signal will follow the same power-law of the reduced power spectrum $E(k_\perp)\sim k^{-\alpha}_\perp$ in the plasma frame, where $\alpha$ 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, $\epsilon=\delta u_0/\sqrt 2 V_\perp$ (where $V_\perp$ is the perpendicular velocity of PSP seen in the plasma frame) and the spectral index $\alpha$.