Shear flow instabilities and Rossby waves in barotropic flow in a rotating annulus

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Abstract
The primary instability of an azimuthal jet is studied experimentally in a rotating annulus with a rigid upper lid (infinite Rossby deformation radius) and a sloping bottom (topographical beta effect). An azimuthal jet is produced by the action of the Coriolis force on fluid pumped between concentric rings of sources and sinks in the bottom of the annulus. The flow is essentially two dimensional by the Taylor–Proudman theorem. Velocity measurements are made with hot‐film probes and particle streak photography. For small forcing flux F, the jet is axisymmetric and has a 1/r velocity profile bounded by narrow free shear layers on each side. At a critical value of F, the inner shear layer becomes unstable to the formation of a propagating chain of vortices; at a larger value of F the outer shear layer also becomes unstable. The critical values of the mode numbers, wave speeds, and F at different annulus rotation rates are in good accord with a linear stability analysis by Lee and Marcus. At onset of instability the vortex chains are similar to those formed by a Kelvin–Helmholtz instability of a free shear layer, but this flow also has some properties typical of a Rossby wave flow—e.g., corotating jets have vortex chains with smaller wave speeds than counter‐rotating jets. This asymmetry is enhanced as F is increased beyond instability onset, since growth in the size of the vortices results in a decrease of Rossby number. At sufficiently large F the vortex chains lock, resulting in a broad wavy jet with the same number of vortices on both sides. For corotating jets these states have significantly smaller wave speeds than the unlocked state, and this small speed is in accord with that predicted for a sinuous Rossby wave. However, the counter‐rotating jets do not satisfy this relation but rather continue to have properties similar to Kelvin–Helmholtz waves.

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