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 hypothesis to magnetohydrodynamic turbulence. We analytically derive one-point two-time correlation functions for Elsässer variables whose Fourier transform yields the corresponding frequency spectra, $E^{\pm }(f)$. We show that $E^{\pm }(f)\propto |{\mathbf{U}}_0\mp {\mathbf{B}}_0{|}^{2/3}$ in Kolmogorov-like model, and $E^{\pm }(f)\propto (B_0|{\mathbf{U}}_0\mp {\mathbf{B}}_0|{)}^{1/2}$ in Iroshnikov-Kraichnan model, where ${\mathbf{U}}_0,{\mathbf{B}}_0$ are the mean velocity and mean magnetic fields respectively.

12 pages

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Cited by in corpus (1)

• Direct power spectral density estimation from structure functions without Fourier transforms