In many space and astrophysical environments, a single source of turbulent energy predominates. This leads to so-called imbalanced MHD turbulence, in which the constituent disturbances move in a prevailing direction.; the solar wind is a particularly well-studied example. Moreover, even globally balanced turbulence spontaneously generates regions where the energies of Alfven waves propagating in opposite directions along the background magnetic field are unequal. Since the development of an MHD turbulent cascade is based on the interaction of waves propagating in opposite directions, it is not obvious that the theory developed for balanced turbulence is applicable to the imbalanced case. This problem is of great interest, and was the subject of a CMSO focused workshop in April 2010.
Numerical simulation of globally balanced MHD turbulence in a large aspect ratio
domain with long axis parallel to the background magnetic field. Red and blue regions
correspond to streams of nonlinear Alfven waves propagating along the background field in
opposite directions. The top panel shows large regions in which one sign of propagation
dominates. In the bottom panel the large scales have been filtered out, revealing fine scale
streams. From S. Boldyrev & J. Perez.
Direct numerical simulations of MHD turbulence supported by analytical theory, reveal that the scaling of the spectra of the counter-propagating Alfven modes do not differ from the balanced case. However, their amplitudes and the corresponding rates of energy cascades are significantly affected by the imbalance. It was also found that a large scale, strongly interacting magnetic field - dubbed a condensate - can form in the presence of imbalanced turbulence, and fundamentally changes its dynamics.