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 degre e of Alfvenicity close to the Sun. Cross-helicity, which is a measure of Al fvenic correlation, tends to decrease with increasing distance from the Sun at high latitudes as well as in slow-speed streams at low latitudes. In th e latter case, large scale inhomogeneities (velocity shears, the heliospher ic current sheet) are present, which are sources of decorrelation; yet at h igh latitudes, the wind is much more homogeneous, and a possible evolution mechanism is represented by the parametric instability. The parametric deca y of an circularly polarized broadband Alfven wave is then investigated, as a source of decorrelation. The time evolution is followed by numerically i ntegrating the full set of nonlinear MHD equations, up to instability satur ation. We find that, for beta similar to 1, the final cross-helicity is sim ilar to 0.5, corresponding to a partial depletion of the initial correlatio n. Compressive fluctuations at a moderate level are also present. Most of t he spectrum is dominated by forward propagating Alfvenic fluctuations, whil e backscattered fluctuations dominate large scales. With increasing time, t he 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.