Nonlinear evolution of the parametric instability: numerical predictions versus observations in the heliosphere

Low-frequency turbulence in the solar wind is characterized by a high degree of Alfvenicity close to the Sun. Cross-helicity, which is a measure of Alfvenic correlation, tends to decrease with increasing distance from the Sun at high latitudes as well as in slow-speed streams at low latitudes. In the latter case, large scale inhomogeneities (velocity shears, the heliospheric current sheet) are present, which are sources of decorrelation; yet at high latitudes, the wind is much more homogeneous, and a possible evolution mechanism is represented by the parametric instability. The parametric decay of an circularly polarized broadband Alfven wave is then investigated, as a source of decorrelation. The time evolution is followed by numerically integrating the full set of nonlinear MHD equations, up to instability saturation. We find that, for beta similar to 1, the final cross-helicity is similar to 0.5, corresponding to a partial depletion of the initial correlation. Compressive fluctuations at a moderate level are also present. Most of the spectrum is dominated by forward propagating Alfvenic fluctuations, while backscattered fluctuations dominate large scales. With increasing time, the spectra of Elsasser variables tend to approach each other. Some results concerning quantities measured in the high-latitude wind are reviewed, and a qualitative agreement with the results of the numerical model is found.