Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910492443803648 |
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| author | Verma, Mahendra K. |
| author_facet | Verma, Mahendra K. |
| contents | 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 |{\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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12790 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind Verma, Mahendra K. Plasma Physics Solar and Stellar Astrophysics Fluid Dynamics Space Physics 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 |{\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. |
| title | Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind |
| topic | Plasma Physics Solar and Stellar Astrophysics Fluid Dynamics Space Physics |
| url | https://arxiv.org/abs/2204.12790 |