Abstract
Abstract. The paper reviews the recent progress on wave turbulence for magnetized plasmas (MHD, Hall MHD and electron MHD) in the incompressible and compressible cases. The emphasis is made on homogeneous and anisotropic turbulence which usually provides the best theoretical framework to investigate space and laboratory plasmas. The solar wind and the coronal heating problems are presented as two examples of application of anisotropic wave turbulence. The most important results of wave turbulence are reported and discussed in the context of natural and simulated magnetized plasmas. Important issues and possible spurious interpretations are also discussed.
Highlights
“The statistical evolution of interacting dispersive waves presents a solvable problem and is free of the closure difficulties associated with the theory of turbulence.” – Benney and Newell (1967)
Zakharov and Filonenko (1966) showed that the wave kinetic equations derived from the wave turbulence analysis have exact equilibrium solutions which are the thermodynamic zero flux solutions and – and more importantly – finite flux solutions which describe the transfer of conserved quantities between sources and sinks
Anisotropic turbulence is well adapted to describe natural magnetized plasmas since a magnetic field is often present on the largest scale of the system, like in the inner interplanetary medium where the magnetic field lines form an Archimedean spiral near the equatorial plane (Goldstein and Roberts, 1999), at the solar surface where coronal loops and open magnetic flux tubes are found (Cranmer et al, 2007) or in planetary magnetospheres where shocks are found (Sahraoui et al, 2006)
Summary
“The statistical evolution of interacting dispersive waves presents a solvable problem and is free of the closure difficulties associated with the theory of turbulence.” – Benney and Newell (1967). The energy transfer between waves occurs mostly among resonant sets of waves and the resulting energy distribution, far from a thermodynamic equilibrium, is characterized by a wide power law spectrum and a high Reynolds number. This range of wavenumbers – the inertial range – is generally localized between large scales at which energy is injected in the system (sources) and small scales at which waves break or dissipate (sinks). We conclude with a discussion in the last Section
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