 
Summary: Threedimensional instability of anticyclonic swirling flow in rotating fluid:
Laboratory experiments and related theoretical predictions
Ya. D. Afanasyev and W. R. Peltier
Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
Received 9 April 1997; accepted 3 September 1998
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 solidbody 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 threedimensional 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 flowthe Rossby number. The evolution of the secondary motions gives rise to the appearance
of tertiary motionswhich are KelvinHelmholtzlike barotropic vortices that develop at the
periphery of the unstable annulus, thus leading to the formation of exceedingly complex dynamical
