  Using an analytic model, we derive the eigenfrequencies for thermal Rossby
waves that are trapped radially and latitudinally in an isentropically
stratified atmosphere. We ignore the star's curvature and work in an equatorial
f-plane geometry. The propagation of inertial waves is found to be sensitive to
the relative direction of the wave vector to the zonal direction. Prograde
propagating thermal Rossby waves are naturally trapped in the radial direction
for frequencies above a critical threshold, which depends on the angle of
propagation. Below the threshold frequency, there exists a continuous spectrum
of prograde and retrograde inertial waves that are untrapped in an isentropic
atmosphere, but can be trapped by gradients in the specific entropy density
such as occurs in a stellar convection zone. Finally, we discuss the
implications of these waves on recent observations of inertial oscillations in
the Sun, as well as in numerical simulations.
