The inrushing/retraction behavior of the Loop Current (LC) in the eastern Gulf of Mexico can be represented by a recurrent cycle of vorticity input/output with a time scale of 0 to 16 months. This cycle is brought about as a balance between the accumulation of absolute vorticity in the LC and deep advection of vorticity to the Caribbean Sea. The vorticity time scale is directly proportional to the change in circulation around the LC and 2πH/Q0(f0 + ζ0); where H (∼800 m) is the thickness of the LC, Q0 is the amplitude of the deep outflow, and (f0 + ζ0) is the absolute vorticity at Yucatan. It is proposed that the vorticity time scale is related to the eddy-shedding period, and this relation suggests that the LC adjusts itself in such a way as to keep 2πH/Q0(f0 + ζ) constant. This parameter captures all relevant processes: thickness of the current, inflow through ζ0 = ∂VI∂x; the deep outflow; and the planetary vorticity (f0).
Lugo-Fernández, A., and A. Badan. 2007. "On the vorticity cycle of the Loop Current." Journal of Marine Research 65, (4). https://elischolar.library.yale.edu/journal_of_marine_research/171