On modulational stability of incompressible magnetohydrodynamic turbulence

Structure formation in magnetohydrodynamic (MHD) turbulence can be modeled as a modulational instability (MI) of the Alfven waves comprising the background turbulence. We focus on the early stages of structure formation (MI's linear stage) and simple backgrounds, such as monochromatic primary waves, in order to develop a tractable model. In particular, we examine the validity of the popular quasilinear approach to the MI, where only two sidebands of a primary wave are retained when analyzing the MI. We find that such truncated models can be fundamentally inadequate in application to ideal MHD. Even at MI's linear stage, the modulational wave energy can propagate up and down the spectrum in the form of dispersive spectral waves which tend to suppress the growth of coherent structures. These waves also introduce unavoidable dissipation of MHD structures, even in the limit of zero viscosity. That said, deviations from ideal MHD that make Alfven waves dispersive tend to reinstate the quasilinear approximation by restricting the spectral-wave propagation and suppressing higher modulational harmonics.