Strong gyres and jets can be generated at auroral latitudes in the thermosphere by enhanced electric fields during geomagnetic substorms. Typical height profiles of ion density suggest that the ion drag force should generate large curvature in the vertical profile of the winds in the highly viscous region of the thermosphere above about 200 km. It is proposed that the poststorm spin-down of these gyres and jets proceeds via Ekman circulations driven by the curvatures in the height profiles of the winds. Analytic and numerical calculations of the ageostrophic winds forced by curvature in model geostrophic wind profiles show that the ageostrophic wind speeds and directions depend mainly on the kinematic viscosity in the region of curvature and the total change in shear in the geostrophic wind. Ageostrophic wind speeds for typical thermospheric jets can exceed 200 m s-1 (about 50% of the jet winds). Spin-down times of thermospheric jets and cyclonic gyres by the Ekman pumping mechanism are estimated at ≲6 hours.