Interplay between turbulence and waves: large-scale helical transfer, and small-scale dissipation and mixing in fluid an
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CLASSICAL AND QUANTUM PLASMAS
Interplay between turbulence and waves: large‑scale helical transfer, and small‑scale dissipation and mixing in fluid and Hall‑MHD turbulence Annick Pouquet1,2 · Duane Rosenberg3 · Julia E. Stawarz4 Received: 4 June 2020 / Accepted: 6 August 2020 © Accademia Nazionale dei Lincei 2020
Abstract Novel features of turbulent flows have been analyzed recently, for example: (1) the possibility of an ideal invariant, such as the energy, to be transferred both to the small scales and to the large scales, in each case with a constant flux; (2) the existence of non-Gaussian wings in Probability Distribution Functions of kinetic, magnetic, and temperature fluctuations, together with their gradients, thus displaying large-scale as well as small-scale intermittency; and (3) the linear dependence on the control parameter of the effective dissipation in turbulence when non-linear eddies and waves interact. We shall briefly review these results with examples stemming from Solar Wind data, the atmosphere and the ocean with either magnetic fields, stratification, and/or rotation. In a second part, we shall examine numerically the inverse cascades of magnetic and of generalized helicity for Hall-MHD in the presence of forcing. These helical invariants in the ideal non-dissipative case involve various cross-correlations between the velocity and vorticity, the magnetic field, and the magnetic potential. For an ion inertial length larger than the forcing scale, the effect of the waves is significant. It leads to an exponential attenuation of the inverse cascade to large scales, since, through the velocity and vorticity, small scales play an increasing dynamical role for a strong Hall current. Keywords Turbulence · Waves · Hall-MHD · Helicity · Inverse cascades
1 Introduction Magnetohydrodynamic (MHD) turbulence differs from ordinary fluid turbulence for several reasons. One of them is the presence of Alfvén waves due to the effect of a uniform, or This paper is a peer-reviewed version of a contribution at the International Conference ‘Plasma Physics and Astrophysics up to 2020 and beyond’ organized by the Department of Physics of Università della Calabria in honor of Pierluigi Veltri’s 70th birthday and held October 7–8, 2019 at Università della Calabria, Rende (Italy). * Annick Pouquet [email protected] 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
288 Harper St., Louisville, CO 80027, USA
4
Department of Physics, Imperial College, London, UK
large-scale, magnetic field, whereas, of course, a uniform velocity field can be eliminated through a Galilean transformation. This leads to a higher degree of non-local interactions, that is interactions between widely separated scales in MHD, and in Hall-MHD in the presence of a Hall current in a generalized Ohm’s law (Alexakis 2007; Mininni et al. 2007) (see, e.g., Mininni et al. (2006) for non-local interactions
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