Bifurcation analysis on flows in a two-layer shallow-water model is used to clarify the dynamical origin of low-frequency variability of the double-gyre wind-driven ocean circulation. In many previous model studies, generic low-frequency variations appear to be associated with distinct regimes, characterized by the level of kinetic energy of the mean flow. From these transient flow computations, the current view is that these regimes, and transitions between them, arise through a complex nonlinear interaction between the mean flow and its high-frequency instabilities (the eddies). On the contrary, we demonstrate here, for a particular (but relevant) case, that the origin of these high- and low-energy states is related to the existence of low-frequency instabilities of steady-state flows. The low-frequency modes have distinct spatial patterns and introduce preferential patterns oscillating on interannual to decadal time scales into the flow. In addition, these lowfrequency modes are shown to be robust to the presence of (idealized) topography; the latter may even have a destabilizing effect.