Abstract
The long-term theoretical “energy paradox” of whether the final state of two merging anticyclones contains more energy than the initial state is studied by considering two typical merging events of ocean mesoscale eddies. The results demonstrate that the total mass (volume), total circulation (area integration of vorticity), and total angular momentum (AM) are conserved if the orbital AM relative to the center of mass is taken into account as the eddies rotate around the center of mass before merging. For subsurface merging, the mass trapped by the Taylor–Proudman effect above the subsurface eddies should also be included. Both conservation laws of circulation and orbital AM have been overlooked in previous theoretical studies. As a result of fusion during merging, the total eddy kinetic energy decreases slightly. In contrast, the total eddy potential energy (EPE) increases after merging. The increase in EPE is mostly supported by the loss of gravitational potential energy (PE) via eddy sinking below the original level prior to merging. This implies that the merging of eddies requires background gravitational PE to be converted to EPE. In contrast, the vorticity and enstrophy consequently decrease after merging. Thus, the eddy merging effect behaves as a “large-scale energy pump” in an inverse energy cascade. It is noted that eddy conservation and conversion laws depend on the laws of physical dynamics, even if additional degrees of freedom can be provided in a mathematical model.