We present the first simulations of the coronal response to Alfv¿n wave injection using transparent boundaries in a classical one-fluid, isothermal axisymmetric model including both closed and open magnetic field structures. The aim of the work is first to study how Alfv¿n waves change the contrast between the equatorial and high-latitude wind, and second, how they modify the geometry of the wind and its global stability. We integrate the full time-dependent MHD equations, and inject large-amplitude (150 km/s), low-frequency (20 min period) waves at 1.8 Rs, both in open and in closed field line regions, except within narrow regions around the poles and the equator. The domain considered extends up to 16 Rs. Our principal results are the following: (1) The assumption of a latitude-independent Alfv¿n wave amplitude compatible with observations leads to a large acceleration both of the high-latitude and equatorial wind; as a consequence, the contrast between slow and fast wind speeds at 16 Rs is not as large as the observed values if extrapolated to 1 AU, a result which could potentially change with the use of better resolved, less dissipative simulations; (2) an initial delay in the Alfv¿n flux onset in one hemisphere generates a stable global circulation in the closed loops region, which after a long enough time produces a global north-south asymmetry and changes the structure of the corona as a whole.