We consider steady solutions of the barotropic quasigeostrophic vorticity equation for a single subtropical gyre with dissipation in the form of lateral friction. Solutions are governed by two parameters: inertial boundary-layer width; and viscous boundary-layer width. Numerical computations for slip conditions indicate a wedge-shaped region in this two-dimensional parameter space, where three solutions coexist. One of these is a viscous solution with weak recirculation; one a solution of intermediate recirculation; and one a strongly nonlinear recirculation gyre. Parametric scalings based on elementary solutions are numerically corroborated as the first and third of these solutions are continued away from the vicinity of the wedge. The multiplicity of solutions is anticipated by a severely truncated Fourier modal representation paralleling Veronis (1963). The Veronis work was originally applied to predict the possibility of multiple solutions in Stommel's (1948) bottom friction model of the circulation. Paradoxically, it appears the solutions are, in that case, unique.
Ierley, Glenn R., and Vitalii A. Sheremet. 1995. "Multiple solutions and advection-dominated flows in the wind-driven circulation. Part I: Slip." Journal of Marine Research 53, (5). https://elischolar.library.yale.edu/journal_of_marine_research/2156