Anisotropic fluxes and nonlocal interactions in MHD turbulence

TL;DR

This study analyzes energy transfer in decaying MHD turbulence with a uniform magnetic field, revealing local transfer functions but nonlocal spectral interactions, especially as magnetic field strength increases, indicating a transition towards weak turbulence.

Contribution

It provides a detailed analysis of local and nonlocal interactions in MHD turbulence, highlighting how magnetic field strength influences the cascade dynamics and mode interactions.

Findings

Transfer functions are local in both parallel and perpendicular directions.

Interactions between counterpropagating Els"asser waves become nonlocal with increasing magnetic field.

Energy flux is dominated by modes with zero parallel wavenumber at high magnetic field strengths.

Abstract

We investigate the locality or nonlocality of the energy transfer and of the spectral interactions involved in the cascade for decaying magnetohydrodynamic (MHD) flows in the presence of a uniform magnetic field $\bf B$ at various intensities. The results are based on a detailed analysis of three-dimensional numerical flows at moderate Reynold numbers. The energy transfer functions, as well as the global and partial fluxes, are examined by means of different geometrical wavenumber shells. On the one hand, the transfer functions of the two conserved Els\"asser energies $E^+$ and $E^-$ are found local in both the directions parallel ($k_\|$-direction) and perpendicular ($k_\perp$-direction) to the magnetic guide-field, whatever the ${\bf B}$-strength. On the other hand, from the flux analysis, the interactions between the two counterpropagating Els\"asser waves become nonlocal. Indeed, as the ${\bf B}$-intensity is increased, local interactions are strongly decreased and the interactions with small $k_\|$ modes dominate the cascade. Most of the energy flux in the $k_\perp$-direction is due to modes in the plane at $k_\|=0$, while the weaker cascade in the $k_\|$-direction is due to the modes with $k_\|=1$. The stronger magnetized flows tends thus to get closer to the weak turbulence limit where the three-wave resonant interactions are dominating. Hence, the transition from the strong to the weak turbulence regime occurs by reducing the number of effective modes in the energy cascade.