Dynamical tides in rotationally flattened planets and stars with stable stratification

Tidal interactions between stars, planets and moons help to shape orbital dynamics in a wide variety of astrophysical systems, but quantitative predictions for tidal distortion and dissipation in gaseous bodies that rotate rapidly remain contentious. I will describe a newly developed numerical method for directly computing tidal dissipation in rotationally flattened planets and stars. Applying this method to critically rotating polytropes and simple models of Jupiter, I will demonstrate that the non-spherical nature of Jupiter's rotation explains anomalous observations of the planet's tidal interaction with its moon, Io. I will additionally discuss the possibility of sustained, resonant tidal dissipation in rotating gaseous bodies, which bears relevance to an extensive range of tidal interactions in astrophysics.