Solar wind expansion effects on the evolution of hydromagnetic turbulence in the interplanetary medium

The effects of the large scale gradients generated by the solar wind expansion are taken into account to estimate the turbulent flux from nonlinear interactions among inward and outward propagating Alfvén waves. It is shown that even if all inward propagating waves are lost in the acceleration region of the wind, nonlinear couplings survive because of scattering effects from the large scale gradients. A new phenomenology is proposed which involves interactions among purely outgoing waves (mediated by secondary scattered incoming fluctuations) and leads to a power spectrum scaling k^-α, α ~ 1, close to what is found in the long-wavelength domain of solar wind fluctuations near the sun. In more general situations, when a nonnegligible amount of ordinary incoming waves are present, the spectral index is determined by the competition between the different contributions to the nonlinear flux, so that the spectral index may vary with wavelength, from α ~ 1 for the largest scales, to α ~ 1.5-1.7 for the small scales.