A quantitative model for the meridional drift of mesoscale eddies: β-dipole advection and eddy interaction

This study develops a quantitative model for the meridional drift of nonlinear mesoscale eddies in a reduced-gravity, quasi-geostrophic framework. The metric is the drift velocity of an eddy centroid defined and tracked by a closed height-anomaly contour. The analysis considers both single-eddy evolution and eddy interaction. As nonlinearity increases, the evolution of an isolated, axisymmetric eddy transitions from Rossby-wave dispersion with minimal meridional deflection to movement as a compact entity with persistent meridional drift. Using the difference between centroid and height-extremum trajectories as a measure of dispersiveness, a practical criterion for the compact-eddy regime is established. For eddies in this regime, a central result is a quantitative relationship that connects the meridional drift to meridional advection of the eddy boundary. When applied to isolated eddies, this relationship accurately captures the temporal variability of the drift velocity in numerical simulations. Decomposition of eddy circulation reveals a well-known secondary, tilted β -dipole (” β -gyres”) structure. The dipole dominates the boundary advection, thereby leading to a direct and validated relationship in which the temporal variability of centroid drift is controlled by the boundary-averaged meridional dipole velocity, with a proportionality factor depending on eddy size. The size dependence also implies that smaller eddies drift more rapidly. Because the boundary-advection formulation is general and could account for mutual advection, the quantitative relationship remains applicable when eddies interact. This general utility is demonstrated by testing against simulations where realistic eddy interaction is permitted.