Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind

TL;DR

This paper extends Taylor's frozen-in hypothesis to magnetohydrodynamic turbulence, deriving analytical relations between frequency and wavenumber spectra for different turbulence models relevant to solar wind studies.

Contribution

The authors generalize Taylor's hypothesis for MHD turbulence and derive analytical expressions for frequency spectra based on mean magnetic and velocity fields.

Findings

Derived frequency spectra for Kolmogorov-like turbulence model.

Derived frequency spectra for Iroshnikov-Kraichnan turbulence model.

Established relations between mean fields and spectral behaviors.

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 Els\"{a}sser variables whose Fourier transform yields the corresponding frequency spectra, $ E^\pm(f) $. We show that $ E^\pm(f) \propto |{\bf U}_0 \mp {\bf B}_0|^{2/3} $ in Kolmogorov-like model, and $ E^\pm(f) \propto (B_0 |{\bf U}_0 \mp {\bf B}_0|)^{1/2} $ in Iroshnikov-Kraichnan model, where $ {\bf U}_0, {\bf B}_0$ are the mean velocity and mean magnetic fields respectively.