Incompressible Homogeneous Anisotropic Turbulence: Magnetohydrodynamic Turbulence

Chapter

Abstract

This chapter deals with magnetohydrodynamic (MHD) turbulence. In addition to coupled effects investigated in Chapter 11, the specificity of the coupling with the fluctuating magnetic field in an electrically conducting field is discussed with care. The Lorentz force is nonlinear, in contrast with Coriolis and boyancy force, so that Alfvèn waves are not only displayed in linearized equations. Wave turbulence theory for alfvènic turbulence is much simpler, however, than inertial wave turbulence in rotating turbulence discussed in Chapter 7. Isotropized EDQNM models are surveyed, and the formalism for a more general anisotropic model is given, in terms of helical and Elsaesser modes. The case of quasi-static MHD, relevant for liquid metal, from industrial devices to the Earth core, is investigated with special care. Incompressibility is implied in the main part, but magnetosonic waves and anelastic approximation are touched upon at the end. In contrast with kinetic helicity, cross-helicity is shown to be very relevant in homogeneous MHD, turbulence, without artificial forcing or initialization.

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Authors and Affiliations

  1. 1.Laboratoire de Mécanique, Modélisation et Procédés Propres, UMR CNRS 7340, Ecole Centrale de MarseilleAix-Marseille UniversitéMarseilleFrance
  2. 2.Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509Ecole Centrale de LyonÉcullyFrance

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