We compare the linear and nonlinear components in the equation of potential vortex conservation based on the altimeter satellite data. We apply the analysis for two regions of the World Ocean in the southern hemisphere. The first region is one of the most dynamically changing regions of the World Ocean and is located to the south of Cape Agulhas. The second area is located in the low latitudes of the Indian Ocean. We show that nonlinear effects predominate in the sea level of low-frequency variability in the regions. This result confirms the earlier conclusion that nearly all features isolated by the method of automatic identification in the sea level are nonlinear. Consequently, the criterion for determining the degree of nonlinearity of structures by comparing the maximum circumferential velocity of particles with the speed of feature displacement is a reliable indicator of nonlinearity. Comparison of linear and nonlinear components of the two regions in Southern Hemisphere has shown that in low latitudes nonlinear effects differ from linear by the order of magnitude. However, these characteristics differ by two orders of magnitude for middle latitudes. We found that in the early studies based on altimetric data researches exaggerated the impact of Rossby waves for the low latitudes of Indian Oceans.