The problem of scaling in isotropic magnetohydrodynamic (MHD) turbulence has remained unresolved, with competing predictions of $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. In this talk I will present results of high-resolution numerical simulations on $8192^2$ and $1024^3$ grids. The computed energy spectra of the total energy, cross helicity, and Elsasser variables are closer to $k^{-5/3}$ than $k^{-3/2}$. More importantly, our detailed analyses of structure functions, intermittency exponents, and energy fluxes demonstrate robust support for Kolmogorov scaling. For example, the fluxes of the Elsasser variables are different for imbalanced MHD, and the third-order structure functions for proportional to $l$. The magnetic energy shows $k^{-5/3}$ spectrum, but the kinetic energy exhibits $k^{-3/2}$ spectrum; the latter spectrum is due to the energy transfers from the magnetic field to the velocity field. We also discuss critical balance and Boldyrev et al.'s dyanmic alignment in relation to anistropic MHD turbulence. Our findings firmly establish Kolmogorov scaling in MHD turbulence, significantly improving the theoretical foundations for modeling astrophysical turbulence and dynamo processes.
*This research used Frontier of the Oak Ridge Leadership Computing Facility (through Director's Discretionary Program) at the Oak Ridge National Laboratory. Simulations were also performed on Param Sanganak (IIT Kanpur), and HPC facility of Kotak School of Sustainability (KSS). Part of this work was supported by Anusandhan National Research Foundation, India (Grant No. SERB/PHY/2021522), and the J. C. Bose Fellowship (SERB /PHY/2023488).
Publication:M. Verma, A. K. Jha, S. Nirgudkar, and M. K. Verma, Numerical Demonstration of Kolmogorov Scaling in Magnetohydrodynamic Turbulence, To appear in Phys. Rev. Fluids (2025) M. Verma, A. K. Jha, and M. K. Verma, Magnetohydrodynamic turbulence follows Kolmogorov scaling, Under review in Phys. Rev. Lett. (2025)
