Abstract
Sloudsky in 1895 and Poincaré in 1910 were the first to derive solutions for the flow driven in the Earth's fluid core by the luni-solar precession. In 1993, Kerswell investigated the stability of this so-called “Poincaré flow” by applying a method devised in 1992 by Ponomarev and Gledzer to study the instability of flows with elliptical streamlines. They represented the components of the perturbed flow by sums of polynomials. Kerswell restricted attention to the linear and quadratic cases. Here cubic, quartic, quintic, and sextic generalizations are developed. Instabilities are located in new areas of parameter space, including some that verge on the small oblateness of the Earth's core
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