Weak Alfven-Wave Turbulence Revisited

TL;DR

This paper revisits weak Alfvén-wave turbulence, revealing distinct spectral behaviors for waves and 2D modes, and explores the transition from weak to strong turbulence under various forcing conditions.

Contribution

It demonstrates the absence of spectral continuity between Alfvén waves and 2D modes and characterizes their spectra and energy transfer mechanisms in different forcing scenarios.

Findings

k^{-2} spectrum for Alfvén waves

k^{-1} spectrum for 2D modes

Transition to strong turbulence at energy equivalence point

Abstract

Weak Alfvenic turbulence in a periodic domain is considered as a mixed state of Alfven waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed and indeed none is found. If the 2D modes are not directly forced, k^{-2} and k^{-1} spectra are found for the Alfven waves and the 2D modes, respectively, with the latter less energetic than the former. The wave number at which their energies become comparable marks the transition to strong turbulence. For imbalanced energy injection, the spectra are similar and the Elsasser ratio scales as the ratio of the energy fluxes in the counterpropagting Alfven waves. If the 2D modes are forced, a 2D inverse cascade dominates the dynamics at the largest scales, but at small enough scales, the same weak and then strong regimes as described above are achieved.