We use a two-dimensional, incompressible MHD spectral code to establish that shear-driven turbulence is a possible means for producing many observed properties of the evolution of the magnetic and velocity fluctuations in the solar wind and, in particular, the evolution of the cross helicity (''Alfv¿nicity'') at small scales. We find that large-scale shear can nonlinearly produce a cascade to smaller scale fluctuations even when the linear Kelvin-Helmholtz mode is stable and that a roughly power law inertial range is established by this process. While the fluctuations thus produced are not Alfv¿nic, they are nearly equipartitioned between magnetic and kinetic energy. We report simulations with Alfv¿nic fluctuations at high wave numbers, both with and without shear layers and find that it is the low cross helicity at low wave numbers that is critical to the cross helicity evolution, rather than the geometry of the flow or the dominance of kinetic energy at large scales. The fluctuations produced by shear effects are shown to evolve similarly but more slowly in the presence of a larger mean field and to be anisotropic with a preferred direction of spectral transfer perpendicular to the mean field. The evolution found is similar to that seen in some other simulations of MHD turbulence, and thus seems in many respects to be an instance of a more generic turbulent evolution rather than due to specific conditions in the solar wind. ¿ American Geophysical Union 1992