Rotating dense currents on a slope. Part 1. Stability

Abstract

Using a novel experimental set-up, we examine the stability of an axisymmetric dense current of fluid on a sloping bottom in a rotating frame of reference. In a cylindrical tank on a rotating table, saline fluid is injected through an annular mesh encircling a cone of 1/15 slope. The resulting ring of fluid becomes unstable to periodic sinusoidal waves, whose characteristics are examined as a function of the ambient fluid depth, the rotation rate, and the salinity and depth of the dense current, the latter being related to the injection time. For experiments with relatively low-salinity currents, we find the phase speed of the instability is proportional to the rotation rate, $\Omega$, rather than being proportional to the Nof speed, which varies as $1/\Omega$. Likewise, the number of waves observed is found to be inconsistent with existing theories for baroclinic instability of a dense current on a sloping bottom with a stationary ambient.

Surface tracers reveal that significant currents are induced in the ambient by the injection of the saline fluid and we propose that it is the coupling between the surface and bottom flow that ultimately controls the observed dynamics. In particular, we propose that barotropic instability of the surface flow controls the behaviour of the low-salinity current and, using potential vorticity conservation, we predict the phase speed of the instability should indeed be proportional to $\Omega$. The experimental results are also compared with related work in which eddies and Ekman layers evolve from dense fluid injected from a localized source.