Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers

The effects of the Coriolis force on the elliptical instability are studied experimentally in cylindrical and spherical rotating containers placed on a table rotating at a fixed rate Ω̃G . For a given set-up, changing the ratio Ω G of global rotation Ω̃G to flow rotation Ω̃F leads to the selection of various unstable modes due to the presence of resonance bands, in close agreement with the normal-mode theory. No instability occurs when Ω G varies between −3/2 and −1/2 typically. On decreasing Ω G toward −1/2, resonance bands are first discretized for Ω G <0 and progressively overlap for −1/2 ≪ Ω G < 0. Simultaneously, the growth rates and wavenumbers of the prevalent stationary unstable mode significantly increase, in quantitative agreement with the viscous short-wavelength analysis. New complex resonances have been observed for the first time for the sphere, in addition to the standard spin-over. We argue that these results have significant implications in geo- and astrophysical contexts.