Magnetohydrodynamic turbulence concerns the chaotic regimes of magnetofluid flow at high Reynolds number.
Magnetohydrodynamics (MHD) deals with what is a quasi-neutral fluid with very high conductivity.
The incompressible MHD equations for constant mass density,
For such flows typically the velocity and the magnetic fields are random.
plays an important role in dynamo (magnetic field generation) problem.
More discussions on MHD turbulence can be found in Biskamp,[1] Verma.
Iroshnikov[3] and Kraichnan[4] formulated the first phenomenological theory of MHD turbulence.
wavepackets travel in opposite directions with the phase velocity of
Later Dobrowolny et al.[5] derived the following generalized formulas for the cascade rates of
as the interaction time scale for the eddies and derived Kolmogorov-like energy spectrum for the Elsasser variables: where
The main underlying assumption in that Iroshnikov and Kraichnan's phenomenology should work for strong mean magnetic field, whereas Marsh's phenomenology should work when the fluctuations dominate the mean magnetic field (strong turbulence).
However, as we will discuss below, the solar wind observations and numerical simulations tend to favour −5/3 energy spectrum even when the mean magnetic field is stronger compared to the fluctuations.
This issue was resolved by Verma[8] using renormalization group analysis by showing that the Alfvénic fluctuations are affected by scale-dependent "local mean magnetic field".
, substitution of which in Dobrowolny's equation yields Kolmogorov's energy spectrum for MHD turbulence.
energy spectra consistent with Kolmogorov-like model for MHD turbulence.
The above renormalization group calculation has been performed for both zero and nonzero cross helicity.
The above phenomenologies assume isotropic turbulence that is not the case in the presence of a mean magnetic field.
are components of the wavenumber parallel and perpendicular to mean magnetic field.
("critical balanced state") which implies that The above anisotropic turbulence phenomenology has been extended for large cross helicity MHD.
Researchers have calculated the energy spectra of the solar wind plasma from the data collected from the spacecraft.
[12][13] The interplanetary and interstellar electron density fluctuations also provide a window for investigating MHD turbulence.
The theoretical models discussed above are tested using the high resolution direct numerical simulation (DNS).
Number of recent simulations report the spectral indices to be closer to 5/3.
Since 5/3 and 3/2 are quite close numerically, it is quite difficult to ascertain the validity of MHD turbulence models from the energy spectra.
can be more reliable quantities to validate MHD turbulence models.
(high cross helicity fluid or imbalanced MHD) the energy flux predictions of Kraichnan and Iroshnikov model is very different from that of Kolmogorov-like model.
[15] Anisotropic aspects of MHD turbulence have also been studied using numerical simulations.
Energy transfer among various scales between the velocity and magnetic field is an important problem in MHD turbulence.
[2] These calculations show a significant energy transfer from the large scale velocity field to the large scale magnetic field.
There are many open challenges in this field that hopefully will be resolved in near future with the help of numerical simulations, theoretical modelling, experiments, and observations (e.g., solar wind).