  Recent observations of Rossby waves and other more exotic forms of inertial
oscillations in the Sun's convection zone have kindled the hope that such waves
might be used as a seismic probe of the Sun's interior. Here we present a 3D
numerical simulation in spherical geometry that models the Sun's convection
zone and upper radiative interior. This model features a wide variety of
inertial oscillations, including both sectoral and tesseral equatorial Rossby
waves, retrograde mixed inertial modes, prograde thermal Rossby waves, the
recently observed high-frequency retrograde (HFR) vorticity modes, and what may
be latitudinal overtones of these HFR modes. With this model, we demonstrate
that sectoral and tesseral Rossby waves are ubiquitous within the radiative
interior as well as within the convection zone. We suggest that there are two
different Rossby-wave families in this simulation that live in different wave
cavities: one in the radiative interior and one in the convection zone.
Finally, we suggest that many of the retrograde inertial waves that appear in
the convection zone, including the HFR modes, are in fact all related, being
latitudinal overtones that are mixed modes with the prograde thermal Rossby
waves.
