The ability of long-wave low-frequency basin modes to be resonantly excited depends on the efficiency with which energy fluxed onto the western boundary can be transmitted back to the eastern boundary. This efficiency is greatly reduced for basins in which the long Rossby wave basin-crossing time is latitude dependent.

In the singular case where the basin-crossing time is independent of latitude, the amplitude of resonantly excited long-wave basin modes grows without bound except for the effects of friction. The speed of long Rossby waves is independent of latitude for quasigeostrophic dynamics, and the rectangular basin geometry often used for theoretical studies of the wind-driven ocean circulation is such a singular case for quasigeostrophic dynamics.

For more realistic basin geometries, where only a fraction of the energy incident on the western boundary can be transmitted back to the eastern boundary, the modes have a finite decay rate that in the limit of weak friction is independent of the choice of frictional parameters. Explicit eigenmode computations for a basin geometry similar to the North Pacific but closed along the equator yield basin modes sufficiently weakly damped that they could be resonantly excited.

The steady-state solutions of a barotropic double-gyre ocean model in which the wind stress curl input of vorticity is balanced primarily by bottom friction are studied. The bifurcations away from a unique and stable steady state are mapped as a function of two nondimensional parameters (δ_I, δ_S), which can be thought of as measuring respectively the relative importance of the nonlinear advection and bottom damping of relative vorticity to the advection of planetary vorticity.

A highly inertial branch characterized by a circulation with transports far in excess of those predicted by Sverdrup balance is present over a wide range of parameters including regions of parameter space where other solutions give more realistic flows. For the range of parameters investigated, in the limit of a large Reynolds number, δ_I/δ_S → ∞, the inertial branch is stable and appears to be unique. This branch is antisymmetric with respect to the midbasin latitude like the prescribed wind stress curl. For intermediate values of δ_I/δ_S, additional pairs of mirror image nonsymmetric equilibria come into existence. These additional equilibria have currents that redistribute relative vorticity across the line of zero wind stress curl. This internal redistribution of vorticity prevents the solution from developing the large transports that are necessary for the antisymmetric solution to achieve a global vorticity balance. Beyond some critical Reynolds number, the nonsymmetric solutions are unstable to time-dependent perturbations. Time-averaged solutions in this parameter regime have transports comparable in magnitude to those of the nonsymmetric steady state branch. Beyond a turning point, where the nonsymmetric steady-state solutions cease to exist, all the computed time-dependent model trajectories converge to the antisymmetric inertial runaway solution. The internal compensation mechanism, which acts through explicitly simulated eddies, is itself dependent upon an explicit dissipation parameter.

The steady-state solutions of a barotropic double-gyre ocean model in which the wind stress curl input of vorticity is balanced primarily by bottom friction are studied. The bifurcations away from a unique and stable steady state are mapped as a function of two nondimensional parameters (δ_I, δ_S), which can be thought of as measuring respectively the relative importance of the nonlinear advection and bottom damping of relative vorticity to the advection of planetary vorticity.

A highly inertial branch characterized by a circulation with transports far in excess of those predicted by Sverdrup balance is present over a wide range of parameters including regions of parameter space where other solutions give more realistic flows. For the range of parameters investigated, in the limit of a large Reynolds number, δ_I/δ_S → ∞, the inertial branch is stable and appears to be unique. This branch is antisymmetric with respect to the midbasin latitude like the prescribed wind stress curl. For intermediate values of δ_I/δ_S, additional pairs of mirror image nonsymmetric equilibria come into existence. These additional equilibria have currents that redistribute relative vorticity across the line of zero wind stress curl. This internal redistribution of vorticity prevents the solution from developing the large transports that are necessary for the antisymmetric solution to achieve a global vorticity balance. Beyond some critical Reynolds number, the nonsymmetric solutions are unstable to time-dependent perturbations. Time-averaged solutions in this parameter regime have transports comparable in magnitude to those of the nonsymmetric steady state branch. Beyond a turning point, where the nonsymmetric steady-state solutions cease to exist, all the computed time-dependent model trajectories converge to the antisymmetric inertial runaway solution. The internal compensation mechanism, which acts through explicitly simulated eddies, is itself dependent upon an explicit dissipation parameter.

The link between low-frequency time-dependent variability and the existence of multiple unstable steady-state solutions in a reduced gravity quasigeostrophic ocean model for the midlatitude wind-driven circulation is investigated. It is shown that a sequence of successive symmetry-breaking pitchfork bifurcations lead to multiple equilibria that differ from each other primarily in the elongation of the recirculation cell, in the amount of meandering present in the intergyre jet, and in a north–south shift in the eastward jet. The elongation of the recirculation cells and the meandering of the jet play compensating roles in the establishment of the global energy and vorticity balance.

The solutions also have distinct energy levels, but general agreement between them and the bumps in a histogram of the total energy obtained from a 1200-yr time-dependent simulation is not found. Nevertheless, a substantial fraction of the variance (30%) can be accounted for by four coherent structures that capture the subspace spanned by four vectors that point from the mean state to four selected fixed points. The steady-state solution with the most elongated recirculation cells acts most strongly in steering the trajectory of the time-dependent model in phase space and sets a rough upper bound on the energy of the flow.

The spectrum of linear free modes of a reduced-gravity ocean in a closed basin with weak dissipation is examined. The constraint of total mass conservation, which in the quasigeostrophic formulation determines the pressure on the boundary as a function of time, allows the existence of selected large-scale, low-frequency basin modes that are very weakly damped in the presence of dissipation.

These weakly damped modes can be quasi-resonantly excited by time-dependent forcing near the eigenperiods, or during the process of adjustment to Sverdrup balance with a steady wind from arbitrary initial conditions. In both cases the frequency of the oscillations is a multiple of 2π/t₀, where t₀ is the long Rossby wave transit time, which is of the order of decades for midlatitude, large-scale basins. These oscillatory modes are missed when the global mass conservation constraint is overlooked.

A model for the interaction between the midlatitude ocean gyres and the wind stress is formulated for a shallow-water, spherical hemisphere with finite thermocline displacement and the latitudinal dependence of the long Rossby wave speed. The oceanic currents create a temperature front at the midlatitude intergyre boundary that is strongest near the western part of the basin. The intergyre temperature front affects the atmospheric temperature gradient in the storm track region, increasing the eddy transport of heat and the surface westerlies. The delayed adjustment of the gyres to the wind stress causes the westerly maximum to migrate periodically in time with a decadal period. The behavior of the model in a spherical geometry is qualitatively similar to that in a quasigeostrophic setting except that here the coupled oscillation involves oceanic temperature anomalies that circulate around the subpolar gyre, whereas the quasigeostrophic calculations favor the subtropical gyre. Another difference is that here there is a linear relationship between the period of the coupled oscillation and the delay time for the adjustment of ocean gyres to changes in the wind stress. This result departs from the quasigeostrophic result, in which the advection timescale also influences the period of the decadal oscillation.