Inertial wave eigenfrequencies for a nonuniformly rotating fluid

A perturbation method is used to calculate the inertial wave eigenfrequencies for an inviscid, nonuniformly rotating fluid. The general results from this calculation for an arbitrary departure from uniform rotation are specialized for differential rotations. The method is checked by verifying that it gave the same result as found analytically for the case of a solid body perturbation. In our analysis the eigenfrequencies are real thus verifying that the differential rotation is a stable perturbation for inertial waves. The method is used to model the experimentally observed collapse of inertial waves near resonance where the differential rotation is a rectified flow. Another application of this work is its extension to the inverse problem of determining the differential rotation of the Earth’s fluid outer core. The recent gravimetric observations of inertial waves detected after large deep earthquakes provide the necessary data for this inversion.