Numerical simulations of the motion of a turbulent homogeneous fluid in a rectangular beta-plane ocean basin are conducted to examine the influence of lateral boundary conditions on the development of inertial circulations. Three different boundary conditions are considered. Firstly, with a condition of zero vorticity gradient normal to the boundary, inertial Fofonoff gyres, which coincide with the maximum entropy solution of statistical mechanics, develop from the release of an initial random eddy field. Secondly, under a condition of no-stress (free-slip) at the boundary, inertial gyres resembling the Fofonoff flow develop. However, in this case, the linear relationship between potential vorticity and streamfunction is not obtained. Rather the potential vorticity is virtually uniform within the recirculating gyres. Finally, with a no-slip boundary, inertial Fofonoff-like gyres are not obtained at moderately high Reynolds number. In stochastically forced simulations with bottom friction, rectified Fofonoff gyres develop which are affected by the boundary conditions in a similar fashion as the freely decaying simulations. The mean gyres are driven by a nonlinear transfer of energy from eddies to the mean flow. No-slip boundaries are effective at defeating this nonlinear transfer. It is shown that the rectified circulation is associated with a systematic flux of eddy potential vorticity directed down the planetary vorticity gradient and along the western boundary.
Patrick F.. 1992. "Inertial gyres in decaying and forced geostrophic turbulence." Journal of Marine Research 50, (4). https://elischolar.library.yale.edu/journal_of_marine_research/2046