Observations of eolian features in the south polar region of Mars show strikingly axisymmetric patterns. Dark streaks and splotches show a pattern spiraling away from the pole in a retrograde direction. Frost streaks appearing in the lee of craters within the polar cap show a spiral away from the pole in a prograde direction. We present an explanation for the patterns in terms of the simplest possible dynamical model. We assume axisymmetric steady flow and adopt the Boussinesq approximation. Atmospheric temperatures are assumed to be known. The vertical exchange of momentum is parametrized in terms of a constant eddy viscosity. The swirl component of the surface stress is controlled by the transfer of angular momentum by the Hadley circulation and by the spin-up or spin-down produced net mass transfer associated with condensation or sublimation of the seasonal CO2 cap. The results show excellent agreement with the observations, suggesting that the important momentum exchange processes have been included in the model. Surface stresses are largest during rapid condensation or sublimation of the cap. Between Ls=40¿ and 140¿ a strong prograde stress field matches the observed frost streak directions. During recession of the CO2 cap the swirl is reversed, and large retrograde surface stresses are predicted between Ls=200¿ and 260¿, consistent with dark streak directions. When the CO2 cap is absent, stresses are greatly reduced.