COMPOSITIONAL CONVECTION IN THE PRESENCE OF ROTATION

The stability of a compositionally buoyant plume, of circular cross-se ction, rising in a rotating infinite fluid is investigated. Both plume and fluid have the same non-zero kinematic viscosity, upsilon, and th ermal diffusivity, kappa. The growth rate of the instability depends o n the Taylor number, Ta (which is a dimensionless number measuring the effect of the Coriolis force relative to the viscous force) and on th e thickness, so, of the plume in addition to the Prandtl number, sigma (= upsilon/kappa) and the Reynolds number, R (which measures the stren gth of the forcing). The analysis is restricted to the case of small R . It is found that the presence of rotation enhances instability. A si mple model of a single interface separating the two parts of an infini te fluid is investigated first in order to isolate the mechanism respo nsible for the increase in the growth rate with rotation. It is shown that the Coriolis force interacts with the zonal velocity component to produce a velocity component normal to the interface. For the right c hoice of wave vector components, this normal velocity component is in phase with the displacement of the interface and this leads to instabi lity. The maximum growth rate is identified in the whole space of the parameters sigma, Ta, s(o) when R << 1. While the maximum growth rate is of order R-2 in the absence of rotation, it is increased to order R in the presence of rotation. It is also found that the Prandtl number , o, which has a strong influence on the growth rate in the absence of rotation, plays a subservient role when rotation is present.