Mesoscale eddies are ubiquitous features in the oceans and dominate the kinetic energy reservoir. They mostly arise from instabilities of large-scale persistent currents and have been routinely observed through satellite altimetry for almost three decades (Chelton et al., 2011). They play an active role in the transport of tracers, yet several questions on the underlying mechanisms of dispersion and their regional and global implications remain debated (e.g., Abernathey & Haller, 2018;Zhang et al., 2014).As put forward in McWilliams (2008), "almost all our understanding of eddy dynamics and phenomena has its roots in quasi-geostrophic theory". Indeed, the dominant instabilities of large-scale currents and the lifecycle of mesoscale eddies are well described by the quasi-geostrophic theory. This theory relies on several assumptions, a fundamental one being that the Rossby number of the flow (Ro), which compares the inertial force to the Coriolis force, is small (Ro < 0.1, e.g., Section 5.3 in Vallis, 2006). In the limit of Ro → 0, there is a perfect symmetry in the phenomenology of cyclones and anticyclones. For Ro = O(0.1), an asymmetry is observed to develop with a dominance of anticyclones over cyclones. Correspondingly, the probability density function of the relative vorticity of the flow is slightly skewed toward negative values (e.g., Polvani et al., 1994). Reasons for this dominance are manifold (see the discussion in Polvani et al., 1994), but the sole kinematic consequence of the emergence of inertial forces is the acceleration of anticyclones and the slowing down of cyclones (Penven et al., 2014). No further kinematic asymmetry emerges from the regime of Ro = O(0.1).Two mechanisms commonly invoked to explain asymmetrical effects in convergence and divergence in cyclones and anticyclones are eddy pumping and Ekman pumping (McGillicuddy, 2016). The former is active toward the beginning and the end of the eddy life cycle (e.g., Figure 4.21 in Flierl & McGillicuddy, 2002). When a