Abstract—The article focuses on the interaction of Rossby waves in the ocean with zonal jet flows. A new approach is proposed to show that nonlinearity in the long-wave approximation exactly compensates the Doppler shift. A new dispersion relation for the Rossby waves interacting with the jets is deduced from the nonlinear theory. The conclusion is verified using satellite altimetry data of the Antarctic Circumpolar Current (ACC). For the ACC area, we compare empirical velocities obtained from the altimetry data with theoretical phase velocities of Rossby waves calculated from nonlinear dispersion relation using the equivalent beta effect. The comparison shows that the new dispersion relation based on the nonlinear approach is capable of describing both the westward and the eastward propagation of mesoscale eddies in the field of sea level anomalies that can be identified as manifestation of Rossby waves in the ocean.