  Three-dimensional equatorial trapped waves excited by stellar isolation and
the resulting equatorial superrotating jet in a vertical stratified atmosphere
of a tidally-locked hot Jupiter are investigated. Taking the hot Jupiter HD
189733b as a fiducial example, we analytically solve a set of linear equations
subject to stationary stellar heating with a uniform zonal-mean flow included.
We also extract wave information in the final equilibrium state of the
atmosphere from the radiative hydrodynamical simulation for HD 189733b by
Dobbs-Dixon & Agol (2013). We find that the analytic wave solutions are able to
qualitatively explain the three-dimensional simulation results. Studying the
vertical structure of waves allows us to explore new wave features such as the
westward tilt of wavefronts related to the Rossby-wave resonance as well as
double gyres of dispersive Rossby waves. We also make an attempt to apply our
linear wave analysis to explain some numerical features associated with the
equatorial jet development seen in the GCM by Showman & Polvani (2011). During
the spin-up phase of the equatorial jet, the acceleration of the jet as a
result of the divergence of the wave momentum flux can be in principle boosted
by the Rossby-wave resonance as the superrotating jet speed is close to the
phase speed of the Rossby waves. However, we also find that as the jet speed
increases, the Rossby-wave structure shifts eastward, while the Kelvin-wave
structure remains approximately stationary, leading to the decline of the
acceleration rate. Our analytic model of jet evolution implies that there
exists only one stable equilibrium state of the atmosphere, possibly implying
that the final state of the atmosphere is independent of initial conditions in
the linear regime. Limitations and future improvements are also discussed.
