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, E±(f). We show that for isotropic turbulence, E±(f)∝|U0 ∓ B0|2/3 in the Kolmogorov-like model and E±(f)∝(B0|U0 ∓ B0|)1/2 in the Iroshnikov–Kraichnan model, where U0 and B0 are the mean velocity and mean magnetic fields, respectively, and f±=k|U0 ∓ B0|/(2π) are the respective frequencies for a wavenumber k. However, for anisotropic magnetohydrodynamic turbulence, E±(f)∝B02/3 when U0≪B0. These results are important for the analysis of solar wind, in particular, those measured by Parker Solar Probe.