Inverse and direct energy cascades in two-dimensional β-plane magnetohydrodynamic turbulence

Abstract:

Numerical studies of two-dimensional β-plane homogeneous decaying magnetohydrodynamic turbulence are presented. Study of fundamental properties of such turbulence allows understanding the evolution of various astrophysical objects from the Sun and stars to planetary systems, galaxies, and galaxy clusters. Qualitative analysis of energy spectra in two-dimensional β-plane MHD allows understanding the cause of inverse cascade in two-dimensional β-plane magnetohydrodynamic turbulence and the formation and dynamics of zonal flows in astrophysical plasma.

The equations of two-dimensional magnetohydrodynamics with the Coriolis force in the β-plane approximation are used for the qualitative analysis and numerical simulation of processes in plasma astrophysics. The results of numerical simulation of two-dimensional β-plane MHD turbulence with a spatial resolution of 4096 × 4096 with different Rossby parameters β are presented.

The formation of Iroshnikov–Kraichnan spectrum is shown in the early stages of evolution of two-dimensional β-plane magnetohydrodynamic turbulence. The direct energy cascade, which is characteristic of the observed Iroshnikov–Kraichnan spectrum, is presented. The self-similarity of the decay of Iroshnikov–Kraichnan spectrum is studied. Violation of the self-similarity of the decay on long time scales and formation of Kolmogorov spectrum is discovered. The inverse cascade of kinetic energy, which is characteristic of the observed Kolmogorov spectrum, provides the formation of zonal flows.

This work was supported by the Russian Foundation for Basic Research (projects no. 19-02-00016 and no. 20-32-90001).