The stability of dipolar gyres on a beta-plane

When a source-sink dipole forces a fluid on a beta-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 Ro(upsilon) = U/(4 beta a(2)) (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 Ro(upsilon) 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 Ro(upsilon), 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 fluid, 1977], is rationalized herein through the stability properties of the zonal central jet that flows between the source and sink. We consider, in turn, (i) the Kuo's [J. Meteor. 1949, 6, 105-122] zero potential vorticity gradient necessary criteria (valid for an infinite zonal jet), (ii) enstrophy budgets and (iii) linear stability analysis of the mean flow. All three methods point out to the enhanced instability of the westward jet. We show that the transition regime has the characteristics of a super critical Hopf bifurcation.