At least at solar minimum, many regions in slow solar wind near the heliospheric current sheet have very low Alfv¿nicity. Motivated by recent suggestions that the interaction of the waves with the observed striated density, temperature, and magnetic field structures in the low Alfv¿nicity regions causes the decay of outward dominance, we have used two- and three-dimensional MHD codes to simulate such situations to determine the evolution. We find that outward propagating waves in the presence of structures become only slightly less Alfv¿nic (unlike observations), and that what were initially parallel propagating waves fairly rapidly become nearly isotropic with a self-similar spectrum typical of turbulence (similar to observations). These simulations suggest that the low Alfv¿nicity regions must arise from some other cause, such as ''microstreams'' that are eradicated as they decrease the Alfv¿nic correlations. ¿ American Geophysical Union 1996