Taylor's frozen-in hypothesis for magnetohydrodynamic turbulence and solar wind

Abstract

In hydrodynamics, Taylor's frozen-in hypothesis connects the wavenumber spectrum to the frequency spectrum of a time series measured in real space. In this paper, we generalize Taylor's frozen-in hypothesis to magnetohydrodynamic turbulence. We analytically derive one-point two-time correlation functions for Elsässer variables whose Fourier transform yields the corresponding frequency spectra, [Formula: see text]. We show that for isotropic turbulence, [Formula: see text] in the Kolmogorov-like model and [Formula: see text] in the Iroshnikov–Kraichnan model, where [Formula: see text] are the mean velocity and mean magnetic fields, respectively, and [Formula: see text] are the respective frequencies for a wavenumber k. However, for anisotropic magnetohydrodynamic turbulence, [Formula: see text] when [Formula: see text]. These results are important for the analysis of solar wind, in particular, those measured by Parker Solar Probe.