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A compact exact law for compressible isothermal Hall magnetohydrodynamic turbulence

Published online by Cambridge University Press:  19 April 2021

Renaud Ferrand Open the ORCID record for Renaud Ferrand [Opens in a new window] ,
Sébastien Galtier Open the ORCID record for Sébastien Galtier [Opens in a new window]  and
Fouad Sahraoui
Renaud Ferrand*
Affiliation:
Laboratoire de Physique des Plasmas, École polytechnique, CNRS, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, F-91128Palaiseau Cedex, France
Sébastien Galtier
Affiliation:
Laboratoire de Physique des Plasmas, École polytechnique, CNRS, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, F-91128Palaiseau Cedex, France Institut Universitaire de France, 75005Paris, France
Fouad Sahraoui
Affiliation:
Laboratoire de Physique des Plasmas, École polytechnique, CNRS, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, F-91128Palaiseau Cedex, France
*
†Email address for correspondence: renaud.ferrand@lpp.polytechnique.fr
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Abstract

Using mixed second-order structure functions, a compact exact law is derived for isothermal compressible Hall magnetohydrodynamic turbulence with the assumptions of statistical homogeneity, time stationarity and infinite kinetic/magnetic Reynolds numbers. The resulting law is written as the sum of a Yaglom-like flux term, with an overall expression strongly reminiscent of the incompressible law, and a pure compressible source. Being mainly a function of the increments, the compact law is Galilean invariant but is dependent on the background magnetic field if one is present. Only the magnetohydrodynamic source term requires multi-spacecraft data to be estimated whereas the other components, which include those introduced by the Hall term, can be fully computed with single-spacecraft data using the Taylor hypothesis. These properties make this compact law more appropriate for analysing both numerical simulations and in situ data gathered in space plasmas, in particular when only single-spacecraft data are available.

Keywords

plasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 2 , April 2021 , 905870220
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

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