The surface layer of the Southern Ocean is subject to the action of wind, waves and currents. We present solutions from a fine-resolution quasi-geostrophic model with surface friction, which is driven by a specified mean and fluctuating wind field, and predicts the surface current, and also the surface Stokes drift due to the wavefield. The resulting flow patterns control the dispersion of particles at the sea surface, and, using a proven Lagrangian algorithm, batches of particles of specified draught can be injected into the flow at various locations and tracked. The simulated patterns are compared with historical data on dispersion and with drift-card and satellite-drogue studies in the Southern Ocean, iceberg tracking and other studies to show the relative importance of dispersion by synoptic variability in the atmosphere and mesoscale eddies in the ocean.