Non-local MHD turbulence

S. V. Nazarenko, Alan C Newell, S. Galtier

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We consider an example of strongly non-local interaction in incompressible magnetohydrodynamic (MHD) turbulence which corresponds to the case where the Alfvén waves travelling in the opposite directions have essentially different characteristic wavelengths. We use two approaches to the dynamics of turbulent Alfvénic wavepackets: the first is a geometrical WKB theory [Phys. Lett. A 165 (1992) 330] and the second one is a three-wave kinetic equation derived for weakly turbulent waves [J. Plasma Phys., in press]. We show that these theories have a common limit of weak turbulence with scale separation in which they both predict the same Fokker-Planck equation for the wave power spectrum. In both cases the packet wavenumbers (and therefore the Lagrangian field-line separations) are allowed to experience order 1 changes. The WKB theory developed here formalises an intuitive geometrical argument of Goldreich and Sridhar [ApJ 485 (1997) 680] and allows one to see where such an intuition leads to a wrong conclusion about the inapplicability of the three-wave kinetic equation for order 1 wavepacket distortions. We show that the exponent of the constant flux non-local spectrum matches the value previously found for local turbulence at the boundary of the locality interval. The relationship between the WKB theory and the weak turbulence theory found in this paper for an ensemble of Alfvén waves seems to be general for three-wave systems.

Original languageEnglish (US)
Pages (from-to)646-652
Number of pages7
JournalPhysica D: Nonlinear Phenomena
Volume152-153
DOIs
StatePublished - May 15 2001
Externally publishedYes

Fingerprint

magnetohydrodynamic turbulence
Magnetohydrodynamics
Turbulence
Kinetic Equation
turbulence
Wave equation
kinetic equations
Nonlocal Interactions
Plasma waves
Fokker Planck equation
Wave power
Kinetics
Fokker-Planck Equation
Power spectrum
Power Spectrum
Locality
Traveling Wave
Fokker-Planck equation
Intuitive
Ensemble

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Non-local MHD turbulence. / Nazarenko, S. V.; Newell, Alan C; Galtier, S.

In: Physica D: Nonlinear Phenomena, Vol. 152-153, 15.05.2001, p. 646-652.

Research output: Contribution to journalArticle

Nazarenko, S. V. ; Newell, Alan C ; Galtier, S. / Non-local MHD turbulence. In: Physica D: Nonlinear Phenomena. 2001 ; Vol. 152-153. pp. 646-652.
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