Parametric Instability in Two-dimensional Alfv{\'e}nic Turbulence

The parametric instability of two-dimensional Alfvenic turbulence has been studied via direct numerical simulations of magnetohydrodynamics. A general form for an Alfvenic fluctuation is derived, with a strongly anisotropic spectrum with respect to a mean magnetic field, typical of the solar wind. Perturbing this solution, an exponential growth of both compressive and backward-propagating Alfvenic fluctuations has been observed. At variance with previous 1D studies, it has been observed that the growth rate tends to increase with the plasma beta. Unstable modes manifest as strongly localized, coherent, field-aligned, stream-like structures, with anticorrelation between magnetic and density fluctuations, in agreement with observations. These results might help us to understand the development of turbulence in the solar wind as well as in stellar winds.