Nonlinear barotropic vortical patterns on a γ-plane are investigated analytically. The solutions describe large-scale Rossby waves rotating anticyclonically with zero circulation. The Rossby waves are predicted to rotate with a specific angular velocity. The stream function–vorticity relation is assumed to be nonlinear, which may lead to a pronounced asymmetry within the pattern. The similarity between the simulated patterns and the Antarctic Circumpolar Wave is highlighted.