Ringdown of inertial waves in a spheroidal shell of rotating fluid

Abstract

The role of inertial waves in the dynamies of the Earth's fluid core has been investigated through laboratory experiments on a spheroidal shell of rotating fluid. In these experiments inertial waves of azimuthal wavenumber 1, Ekman number 0(10 −5), Rossby number 0(10 −1) were excited by precession of an inner spheroidal body. Proximity to resonance was achieved by adjusting the ratio of the frequency of precession of the inner body to the rotational speed of the container to be near the eigenfrequency of the inertial wave mode being studied. Once the system was near resonance the perturbation was stopped and ringdown records were obtained. Amplitude, eigenfrequency and decay rate were recovered simultaneously for the principal and neighbouring modes excited using an iterative linearized least squares procedure. The recovery of complex eigenfrequencies for non-axisymmetric inertial waves in this shell geometry has given experimental verification of their existence. For those waves of azimuthal wavenumber one, a significant nonlinear interaction among modes is inferred from the simultaneous recovery of neighbouring modes. Other non linear effects include a mean azimuthal flow which appears to be stable for the low spatial order modes studied. These results contrast with highly unstable mean flow found experimentally in similar experiments carried out in cylindrical geometry.