THE INSTABILITY OF A TWO-LAYERED SYSTEM ENCLOSED BETWEEN HORIZONTAL, COAXIALLY ROTATING PLATES

Abstract

The motion of two homogeneous layers of fluid enclosed between horizontal plates, which rotate coaxially at slightly different angular velocities, has been investigated. The solution for the zonally symmetric forced motion is only a slight modification of a solution of Stewartson's (1953) for a single fluid between rotating disks. Experiments with the two-layer system confirmed the existence of symmetric motion, but for a certain range of parameters it was unstable. A criterion for instability of the symmetric flow was developed from appropriate inviscid, quasi-geostrophic frequency equations, using an approximate variational method. A comparison with experiment indicated stability for somewhat greater shear across the interface of the two layers than predicted. Exploratory experiments in the unstable range demonstrated that the number of disturbances tended to increase directly as the rotation rate and inversely with the density difference. A steady wave pattern was observed only when the horizontal dimensions of the disturbance were comparable to the diameter of the cylindrical container. The shape of the steady disturbance was such as to give a strong transport of momentum inward. Certain analogies are drawn between eddy circulation observed in the experiments and low-level cyclones in the atmosphere and meanders of upper-level ocean currents.