Flow regimes in a wide ‘sliced-cylinder’ model of homogeneous beta-plane circulation

Abstract

We report new experiments with the ‘sliced-cylinder’ β-plane model of Pedlosky & Greenspan (1967) and Beardsley (1969), but with a much wider basin such that the western boundary current and its eddies occupy a small fraction of the basin width. These experiments provide new insights into nonlinear aspects of the flow: the critical conditions for boundary current separation and the transition from stable to unstable flow are redefined, and a further transition from periodic to chaotic eddy shedding under strong anticyclonic forcing is also found. In the nonlinear regimes the western boundary current separates from the western wall and shoots into the interior as a narrow jet that undergoes a rapid adjustment to join with the broad slow interior flow. In the unstable regimes this adjustment involves eddy shedding. Each transition occurs at a fixed critical value of a Reynolds number Re_γ based on the velocity and width scales for a purely viscous boundary current: the flow is unstable for Re_γ > 123±4 and aperiodic for Re_γ > 231±5. The results provide evidence that the mechanism causing instability is shear in the separated jet rather than the breaking of a large-amplitude Rossby wave. A quasi-geostrophic numerical model applied to the laboratory conditions yields a stability boundary and detailed characteristics of the flow largely consistent with those determined from the experiments. It also reveals a strong dependence of the circulation pattern on basin aspect ratio, and shows that an adverse higher-order pressure gradient is responsible for western boundary current separation in this model. Eddy–eddy interactions and feedback of fluctuations from the eddy formation region to upstream parts of the boundary current contribute to aperiodic behaviour. As a result of eddy shedding, passive tracer from each streamline in the boundary current can be stirred across much of the width of the basin.