On the interpretation of Parker Solar Probe Turbulent Signals. (arXiv:1906.05644v1 [astro-ph.SR]). Bourouaine, S. & Perez, J. C arXiv Solar and Stellar Astrophysics, July, 2019. ![On the interpretation of Parker Solar Probe Turbulent Signals. (arXiv:1906.05644v1 [astro-ph.SR]) [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex In this letter we propose a practical methodology to interpret future Parker Solar Probe (PSP) turbulent time signals even when Taylor's hypothesis is not valid. By extending Kraichnan's sweeping model used in hydrodynamics we derive the Eulerian spacetime correlation function in magnetohydrodynamics (MHD) turbulence. It is shown that in MHD, the temporal decorrelation of small-scale fluctuations arises from a combination of hydrodynamic sweeping induced by large-scale fluid velocity ${\}delta u_0$ and by the Alfv\'enic propagation along the local magnetic field. The resulting temporal part of the space-time correlation function is used to determine the wavenumber range ${\}Delta k_{\}perp=[k_\{{\}rm min\},k_\{{\}rm max\}]$ of the turbulent fluctuations that contribute to the power of a given frequency ${\}omega$ of the time signal measured in the spacecraft frame. Our analysis also shows that the shape of frequency power spectrum $P_\{sc\}({\}omega)$ of the time signal will follow the same power-law of the reduced power spectrum $E(k_{\}perp){\}sim k{\textasciicircum}\{-{\}alpha\}_{\}perp$ in the plasma frame, where ${\}alpha$ is the spectral index. The proposed framework for the analysis of PSP time signals entirely relies on two simple dimensionless parameters that can be empirically obtained from PSP measurements, namely, ${\}epsilon={\}delta u_0/{\}sqrt 2 V_{\}perp$ (where $V_{\}perp$ is the perpendicular velocity of PSP seen in the plasma frame) and the spectral index ${\}alpha$.
@article{bourouaine_interpretation_2019,
title = {On the interpretation of {Parker} {Solar} {Probe} {Turbulent} {Signals}. ({arXiv}:1906.05644v1 [astro-ph.{SR}])},
url = {http://arxiv.org/abs/1906.05644?utm_source=researcher_app&utm_medium=referral&utm_campaign=RESR_MRKT_Researcher_inbound},
doi = {arXiv:1906.05644v1},
abstract = {In this letter we propose a practical methodology to interpret future Parker
Solar Probe (PSP) turbulent time signals even when Taylor's hypothesis is not
valid. By extending Kraichnan's sweeping model used in hydrodynamics we derive
the Eulerian spacetime correlation function in magnetohydrodynamics (MHD)
turbulence. It is shown that in MHD, the temporal decorrelation of small-scale
fluctuations arises from a combination of hydrodynamic sweeping induced by
large-scale fluid velocity \${\textbackslash}delta u\_0\$ and by the Alfv{\textbackslash}'enic propagation along
the local magnetic field. The resulting temporal part of the space-time
correlation function is used to determine the wavenumber range \${\textbackslash}Delta
k\_{\textbackslash}perp=[k\_\{{\textbackslash}rm min\},k\_\{{\textbackslash}rm max\}]\$ of the turbulent fluctuations that
contribute to the power of a given frequency \${\textbackslash}omega\$ of the time signal
measured in the spacecraft frame. Our analysis also shows that the shape of
frequency power spectrum \$P\_\{sc\}({\textbackslash}omega)\$ of the time signal will follow the
same power-law of the reduced power spectrum \$E(k\_{\textbackslash}perp){\textbackslash}sim k{\textasciicircum}\{-{\textbackslash}alpha\}\_{\textbackslash}perp\$
in the plasma frame, where \${\textbackslash}alpha\$ is the spectral index. The proposed
framework for the analysis of PSP time signals entirely relies on two simple
dimensionless parameters that can be empirically obtained from PSP
measurements, namely, \${\textbackslash}epsilon={\textbackslash}delta u\_0/{\textbackslash}sqrt 2 V\_{\textbackslash}perp\$ (where \$V\_{\textbackslash}perp\$ is
the perpendicular velocity of PSP seen in the plasma frame) and the spectral
index \${\textbackslash}alpha\$.},
journal = {arXiv Solar and Stellar Astrophysics},
author = {Bourouaine, Sofiane and Perez, Jean C},
month = jul,
year = {2019},
keywords = {Researcher App, ⚠️ Invalid DOI},
}
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It is shown that in MHD, the temporal decorrelation of small-scale fluctuations arises from a combination of hydrodynamic sweeping induced by large-scale fluid velocity ${\\}delta u_0$ and by the Alfv\\'enic propagation along the local magnetic field. The resulting temporal part of the space-time correlation function is used to determine the wavenumber range ${\\}Delta k_{\\}perp=[k_\\{{\\}rm min\\},k_\\{{\\}rm max\\}]$ of the turbulent fluctuations that contribute to the power of a given frequency ${\\}omega$ of the time signal measured in the spacecraft frame. Our analysis also shows that the shape of frequency power spectrum $P_\\{sc\\}({\\}omega)$ of the time signal will follow the same power-law of the reduced power spectrum $E(k_{\\}perp){\\}sim k{\\textasciicircum}\\{-{\\}alpha\\}_{\\}perp$ in the plasma frame, where ${\\}alpha$ is the spectral index. The proposed framework for the analysis of PSP time signals entirely relies on two simple dimensionless parameters that can be empirically obtained from PSP measurements, namely, ${\\}epsilon={\\}delta u_0/{\\}sqrt 2 V_{\\}perp$ (where $V_{\\}perp$ is the perpendicular velocity of PSP seen in the plasma frame) and the spectral index ${\\}alpha$.","journal":"arXiv Solar and Stellar Astrophysics","author":[{"propositions":[],"lastnames":["Bourouaine"],"firstnames":["Sofiane"],"suffixes":[]},{"propositions":[],"lastnames":["Perez"],"firstnames":["Jean","C"],"suffixes":[]}],"month":"July","year":"2019","keywords":"Researcher App, ⚠️ Invalid DOI","bibtex":"@article{bourouaine_interpretation_2019,\n\ttitle = {On the interpretation of {Parker} {Solar} {Probe} {Turbulent} {Signals}. ({arXiv}:1906.05644v1 [astro-ph.{SR}])},\n\turl = {http://arxiv.org/abs/1906.05644?utm_source=researcher_app&utm_medium=referral&utm_campaign=RESR_MRKT_Researcher_inbound},\n\tdoi = {arXiv:1906.05644v1},\n\tabstract = {In this letter we propose a practical methodology to interpret future Parker\nSolar Probe (PSP) turbulent time signals even when Taylor's hypothesis is not\nvalid. By extending Kraichnan's sweeping model used in hydrodynamics we derive\nthe Eulerian spacetime correlation function in magnetohydrodynamics (MHD)\nturbulence. It is shown that in MHD, the temporal decorrelation of small-scale\nfluctuations arises from a combination of hydrodynamic sweeping induced by\nlarge-scale fluid velocity \\${\\textbackslash}delta u\\_0\\$ and by the Alfv{\\textbackslash}'enic propagation along\nthe local magnetic field. The resulting temporal part of the space-time\ncorrelation function is used to determine the wavenumber range \\${\\textbackslash}Delta\nk\\_{\\textbackslash}perp=[k\\_\\{{\\textbackslash}rm min\\},k\\_\\{{\\textbackslash}rm max\\}]\\$ of the turbulent fluctuations that\ncontribute to the power of a given frequency \\${\\textbackslash}omega\\$ of the time signal\nmeasured in the spacecraft frame. Our analysis also shows that the shape of\nfrequency power spectrum \\$P\\_\\{sc\\}({\\textbackslash}omega)\\$ of the time signal will follow the\nsame power-law of the reduced power spectrum \\$E(k\\_{\\textbackslash}perp){\\textbackslash}sim k{\\textasciicircum}\\{-{\\textbackslash}alpha\\}\\_{\\textbackslash}perp\\$\nin the plasma frame, where \\${\\textbackslash}alpha\\$ is the spectral index. The proposed\nframework for the analysis of PSP time signals entirely relies on two simple\ndimensionless parameters that can be empirically obtained from PSP\nmeasurements, namely, \\${\\textbackslash}epsilon={\\textbackslash}delta u\\_0/{\\textbackslash}sqrt 2 V\\_{\\textbackslash}perp\\$ (where \\$V\\_{\\textbackslash}perp\\$ is\nthe perpendicular velocity of PSP seen in the plasma frame) and the spectral\nindex \\${\\textbackslash}alpha\\$.},\n\tjournal = {arXiv Solar and Stellar Astrophysics},\n\tauthor = {Bourouaine, Sofiane and Perez, Jean C},\n\tmonth = jul,\n\tyear = {2019},\n\tkeywords = {Researcher App, ⚠️ Invalid DOI},\n}\n\n","author_short":["Bourouaine, S.","Perez, J. 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