Interplay between turbulence and waves: large-scale helical transfer, and small-scale dissipation and mixing in fluid and Hall-MHD turbulence

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.

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Availability of data and material

The authors declare that the calculation material is available upon request.

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Acknowledgements

This text emanates from the talk given by one of us (AP) at the meeting held in honor of PierLuigi Veltri in October 2019 at the University of Calabria in Cosenza (Italy). It is a pleasure to acknowledge the many facets of his work, a little part of which is evoked here in the context of specific Solar Wind theoretical models and observations, and to reminisce about our discussions on many issues of MHD turbulence and on the complexity of the behavior of such systems. The runs analyzed in this paper have used an open allocation on the Janus super-computer at LASP/CU, which is gratefully acknowledged. NCAR is supported by the National Science Foundation. Support for AP, from LASP and in particular from Bob Ergun, is gratefully acknowledged as well.

Funding

The work of Julia E. Stawarz was supported in part by the project UKR/STFC Grant ST/S000364/1.

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Correspondence to Annick Pouquet.

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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).

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Pouquet, A., Rosenberg, D. & Stawarz, J.E. Interplay between turbulence and waves: large-scale helical transfer, and small-scale dissipation and mixing in fluid and Hall-MHD turbulence. Rend. Fis. Acc. Lincei 31, 949–961 (2020). https://doi.org/10.1007/s12210-020-00951-5

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Keywords

  • Turbulence
  • Waves
  • Hall-MHD
  • Helicity
  • Inverse cascades