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Open AccessArticle

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

by Annick Pouquet 1,2,*,†, Julia E. Stawarz 3,† and Duane Rosenberg 4
1
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, USA
2
National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA
3
Department of Physics, Imperial College London, London SW7 2BU, UK
4
288 Harper St., Louisville, CO 80027, USA
*
Author to whom correspondence should be addressed.
Both authors contributed equally to this work.
Atmosphere 2020, 11(2), 203; https://doi.org/10.3390/atmos11020203 (registering DOI)
Received: 5 January 2020 / Revised: 28 January 2020 / Accepted: 1 February 2020 / Published: 14 February 2020
In turbulence, for neutral or conducting fluids, a large ratio of scales is excited because of the possible occurrence of inverse cascades to large, global scales together with direct cascades to small, dissipative scales, as observed in the atmosphere and oceans, or in the solar environment. In this context, using direct numerical simulations with forcing, we analyze scale dynamics in the presence of magnetic fields with a generalized Ohm’s law including a Hall current. The ion inertial length ϵ H serves as the control parameter at fixed Reynolds number. Both the magnetic and generalized helicity—invariants in the ideal case—grow linearly with time, as expected from classical arguments. The cross-correlation between the velocity and magnetic field grows as well, more so in relative terms for a stronger Hall current. We find that the helical growth rates vary exponentially with ϵ H , provided the ion inertial scale resides within the inverse cascade range. These exponential variations are recovered phenomenologically using simple scaling arguments. They are directly linked to the wavenumber power-law dependence of generalized and magnetic helicity, k - 2 , in their inverse ranges. This illustrates and confirms the important role of the interplay between large and small scales in the dynamics of turbulent flows.
Keywords: Turbulence; Helicity; Inverse cascades; Hall Magnetohydrodynamic (Hall-MHD) Turbulence; Helicity; Inverse cascades; Hall Magnetohydrodynamic (Hall-MHD)
MDPI and ACS Style

Pouquet, A.; Stawarz, J.E.; Rosenberg, D. Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale. Atmosphere 2020, 11, 203.

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