Effects of the Radial Law of Depth on the Instability of Inertia Oscillations in Rotating Fluids

Abstract

Systematic changes in the finite-amplitude vortex instability of axisymmetric elastoid-inertia oscillations in circular bodies of fluid with a quadratic law of depth are shown to occur depending on whether the depth increases or decreases radially. The instability is a new type that may have an essentially invicid mechanism and suggestions are made as to possible connections with atmospheric general circulation instability mechanisms. Phase speed measurements of certain observed propagating waves compared with several theoretical estimates suggest very strongly that they are Rossby waves excited by some conversion mechanism from the original inertia modes.