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

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 Elsasser variables whose Fourier transform yields the corresponding frequency spectra, E-+/-(f). We show that for isotropic turbulence, E-+/-(f) proportional to |U-0 -/+ B-0|(2/3) in the Kolmogorov-like model and E (+/-) (f) proportional to (B-0|U-0 -/+ B-0|)(1/2) in the Iroshnikov-Kraichnan model, where U-0 and B-0 are the mean velocity and mean magnetic fields, respectively, and f(+/-) = k|U-0 -/+ B-0|/(2 pi) are the respective frequencies for a wavenumber k. However, for anisotropic magnetohydrodynamic turbulence, E-+/- (f) proportional to B-0(2/3) when U-0 << B-0. These results are important for the analysis of solar wind, in particular, those measured by Parker Solar Probe.