The evolution of MHD fluctuations advected by the solar wind is profoundly affected by the spherical wind expansion: the latter in an important source of anisotropy, the solar plasma becoming increasingly stretched in the transverse direction as it recedes from the sun. As a consequence, the nonlinear evolution of compressive velocity fluctuations in the transverse direction is ‘‘frozen’’ at a finite time in the low frequency limit; at higher frequencies the evolution, e.g., of Alfve´n waves, is easily predicted only in the linear limit. In the fully three‐dimensional and nonlinear case, numerical simulations are necessary: here we present preliminary numerical results from simulations of MHD turbulence in a plasma volume expanding with the wind.