The ventilated thermocline model of Luyten et al. (hereafter LPS), (1983) is reformulated in the quasigeostrophic approximation. The quasigeostrophic solutions with zonal outcrop lines capture the salient features of the solutions of LPS. When the outcrop lines are sufficiently nonzonal, the quasigeostrophic solutions resemble those of Parsons (1969), Veronis (1973), and Huang (1984), resolving an inconsistency in Parsons' solution. But an attempt to close the quasigeostrophic solution having two moving layers with a western boundary current in which friction is parameterized as a linear drag coefficient results in an ill posed problem. The paper concludes with a comparison of cross-gyre ventilation in the quasigeostrophic and LPS formulations.
Hendershott, Myrl C.. 1989. "The ventilated thermocline in quasigeostrophic approximation." Journal of Marine Research 47, (1). https://elischolar.library.yale.edu/journal_of_marine_research/1921