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Normal mode oscillations in Saturn excite density and bending waves in the CRing, providing a valuable window into the planet's interior. Saturn'sfundamental modes (f modes) excite the majority of the observed waves, whilegravito-inertial modes (rotationally modified g modes) associated with stablestratification in the deep interior provide a compelling explanation foradditional density waves with low azimuthal wavenumbers m. However, multipletsof density waves with nearly degenerate frequencies, including an m=3 triplet,still lack a definitive explanation. We investigate the effects of rapid anddifferential rotation on Saturn's oscillations, calculating normal modes forindependently constrained interior models. We use a non-perturbative treatmentof rotation that captures the full effects of the Coriolis and centrifugalforces, and consequently the mixing of sectoral f modes with g modescharacterized by very different spherical harmonic degrees. Realistic profilesfor differential rotation associated with Saturn's zonal winds can enhancethese mode interactions, producing detectable oscillations with frequenciesseparated by less than 1%. Our calculations demonstrate that a three-modeinteraction involving an f mode and two g modes can feasibly explain the finelysplit m=3 triplet, although the fine-tuning required to produce such aninteraction generally worsens agreement with seismological constraints providedby m=2 density waves. Our calculations additionally demonstrate that sectoral fmode frequencies are measurably sensitive to differential rotation in Saturn'sconvective envelope. Finally, we find that including realistic equatorialantisymmetry in Saturn's differential rotation profile couples modes with evenand odd equatorial parity, producing oscillations that could in principleexcite both density and bending waves simultaneously.

Constraining Saturn's interior with ring seismology: effects of differential rotation and stable stratification