The stability of dipolar gyres on a beta-plane

When a source-sink dipole forces a fluid on a β-plane limited by a western boundary, the linear steady solution can be obtained analytically and consists of zonally elongated gyres that extend west of the forcing and close as western boundary currents. The nondimensional parameter Rov=U/(4βa2) (with U the zonal velocity of the flow and 2a the distance between the source and sink) is used to characterize the nonlinearity of the flow. When Rov reaches 0.1, the numerical shallow-water solution shows that the configuration with the source to the north of the sink becomes unstable, while the reverse configuration remains steady. Indeed, that reverse configuration remains steady for much larger values of the nonlinearity parameter Rov, and begins to share some of the characteristics of a pure inertial circulation. The asymmetry of the stability properties of the two configurations, also found in the laboratory experiments of Colin de Verdiere [Quasigeostrophic flows and turbulence in a rotating homogeneous flui...