Magnetohydrodynamic turbulence follows Kolmogorov scaling

The two leading models of isotropic magnetohydrodynamic (MHD) turbulence have competing predictions: $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. This paper identifies the valid MHD turbulence model using high-resolution numerical simulations and diagnostics—structure functions, intermittency exponents, and energy spectra and fluxes of imbalanced MHD. The energy spectra of our forced MHD simulations on $8192^2$ and $1024^3$ grids support Kolmogorov's $k^{-5/3}$ spectrum over Iroshnikov-Kraichnan’s $k^{-3/2}$ spectrum for the Elsasser variables and the total energy. Note, however, that the spectra of the magnetic field or the velocity field may differ from $k^{5/3}$ due to the cross transfers between the magnetic and velocity fields. The difference in the spectral exponents 5/3 and 3/2 is small, hence they are not conclusive. Therefore, we resort to other diagnostics.

The energy fluxes of the imbalanced MHD follow the predictions of Kolmogorov scaling rather than the Iroshnikov-Kraichnan prediction. That is, the dominant field among the Elsasser variables has a larger energy flux than the weaker one. In addition, the numerically computed third-order structure functions and intermittency exponents support Kolmogorov scaling (predictions of Politano and Pouquet) in both two and three dimensions. These results are significant as they would help in a better modelling of solar wind, solar corona, and dynamos.