Interaction of shear-Alfvén wave packets: Implication for weak magnetohydrodynamic turbulence in astrophysical plasmas

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Abstract

The nonlinear interaction of shear-Alfvéan wave packets is a fundamental physical process underlying incompressible magnetohydrodynamics turbulence, as emphasized in the Iroshnikov-Kraichnan theory. In the weak turbulence limit, we give a detailed analytical and numerical treatment of the interaction between two colliding shear-Alfvén wave packets in the presence of a strong and uniform magnetic field B = B0 ẑ. Using the ideal MHD equations, it is shown that three-wave interactions are generally nonzero if the kz = 0 Fourier components of the wave packets are nonzero. From the reduced MHD equations, we calculate in closed form the three-wave and four-wave interaction terms, and show the latter to be generally asymptotically subdominant if the wave packets have no kz = 0 component. Our results on the generic dominance of three-wave interactions contradict recent claims by Sridhar & Goldreich (1994) who have argued that three-wave interactions are empty and that the Iroshnikov-Kraichnan theory is incorrect because it describes weak three-wave turbulence. The principal implication of our results is that the Iroshnikov-Kraichnan theory is still a suitable point of departure for the study of Alfvénic turbulence in the interstellar medium.

Original languageEnglish (US)
Pages (from-to)845-854
Number of pages10
JournalAstrophysical Journal
Volume465
Issue number2 PART I
DOIs
StatePublished - Jan 1 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Keywords

  • MHD
  • Plasmas
  • Turbulence
  • Waves

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