Numerical Demonstration of Kolmogorov Scaling in Magnetohydrodynamic Turbulence

Abstract: 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 and diagnostics-structure functions, intermittency exponents, and energy spectra and fluxes of imbalance MHD. The energy spectra of our forced MHD simulations on $8192^2$, $4096^2$, $1024^3$, and $512^3$ support Kolmogorov's k^{-5/3} spectrum over Iroshnikov-Kraichnan's k^{-3/2} spectrum, but the difference in the spectral exponents is small. However, the numerically computed third-order structure functions and intermittency exponents support Kolmogorov scaling in both two and three dimensions. Also, the energy fluxes of the imbalance MHD follow the predictions of Kolmogorov scaling. These results would help in better modelling of solar wind, solar corona, and dynamos.