Inertial/kinetic-Alfvén wave turbulence: A twin problem in the limit of local interactions

Sébastien Galtier and Vincent David
Phys. Rev. Fluids 5, 044603 – Published 23 April 2020

Abstract

Inertial and kinetic-Alfvén wave turbulences have a priori little in common: indeed, the first one concerns rotating hydrodynamics in the limit of a small Rossby number (with Ω0 the rotating rate) while the second describes high frequency plasmas in the limit of a strong uniform magnetic field B0. In this paper we show analytically that, in the limit of local interactions in the perpendicular direction to Ω0, the inertial wave turbulence equation converges towards the same nonlinear diffusion equation as for kinetic-Alfvén waves when the same limit is taken; the only difference resides in the constants in front of the equations. Therefore, both systems share the same physical properties for the stationary phase with an energy spectrum in k5/2; it is preceded by a self-similar solution of the second kind during the nonstationary phase with a spectrum proportional to k8/3 which propagates explosively towards small scales. It is suggested that the proximity between these two problems may be used to better understand inertial or kinetic-Alfvén wave turbulence.

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  • Received 20 December 2019
  • Accepted 30 March 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.044603

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsPlasma Physics

Authors & Affiliations

Sébastien Galtier1,2,* and Vincent David1,3

  • 1Laboratoire de Physique des Plasmas, École polytechnique, F-91128 Palaiseau Cedex, France
  • 2Université Paris-Saclay, Institut Universitaire de France, IPP, CNRS, Observatoire Paris-Meudon, France
  • 3Université Paris-Saclay, IPP, CNRS, Observatoire Paris-Meudon, France

  • *Corresponding author: sebastien.galtier@lpp.polytechnique.fr

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Vol. 5, Iss. 4 — April 2020

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