atmosphere Article Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale 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;
[email protected] 4 288 Harper St., Louisville, CO 80027, USA;
[email protected] * Correspondence:
[email protected] † Both authors contributed equally to this work. Received: 5 January 2020; Accepted: 1 February 2020; Published: 14 February 2020 Abstract: 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 eH 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 eH, provided the ion inertial scale resides within the inverse cascade range.