Three-dimensional instability of anticyclonic swirling flow in rotating fluid: Laboratory experiments and related theoretical predictions

We present results from a new series of experiments on the geophysically important issue of the instability of anticyclonic columnar vortices in a rotating fluid in circumstances such that the Rossby number exeeds unity. The core of the vortex is modeled as a solid cylinder rotating in a fluid that is itself initially in a state of solid-body rotation. When the cylinder rotates cyclonically the flow induced by the differential rotation is stable except for a brief initial period. When the cylinder rotates anticyclonically, however, intense perturbations spontaneously appear and amplify in the flow. The experimental results demonstrate that secondary motions appear in an annular region of finite width surrounding the cylinder (in accord with the prediction of the generalized Rayleigh criterion) and are governed by the process of three-dimensional centrifugal instability. These motions are characterized by a definite wave number in the coordinate direction parallel to the axis of the cylinder. Both the width of the unstable annular region and the vertical wavelength of the motions induced by centrifugal instability are determined by the main nondimensional parameter of the flow-the Rossby number. The evolution of the secondary motions gives rise to the appearance of tertiary motions-which are Kelvin-Helmholtz-like (barotropic) vortices that develop at the periphery of the unstable annulus, thus leading to the formation of exceedingly complex dynamical structures. If the rotating cylinder is withdrawn vertically from the fluid, the instability rapidly destroys the core of the vortex. During its initial phase of development the flow evolves in a way that, is strongly analogous to the cylindrical Couette case. An appropriate theory is employed to explain the results of the laboratory experiments. (C) 1998 American Institute of Physics. [S1070-6631(98)02812-8].