Professor Ping Zhu, Major ProfessorThis study aims to advance our understanding of the inner-core dynamics of tropical cyclones (TCs) from the perspective of vortex Rossby waves (VRWs) through investigating wave kinematics, propagation feature, and wave-mean-flow interaction in three dimensional TC-like baroclinic vortices. Using the Wenzel-Kramers-Brillouin analysis in the asymmetric balanced model framework, the generalized wave dispersion relation, group velocities, and stagnation radius/height of VRW wave-packets in both pseudo-height and isentropic coordinates are derived. It is found that the VRW dispersion relation associated with baroclinic vortices in an isentropic coordinate has the same format as that of barotropic vortices in a pseudo-height coordinate. However, baroclinicity causes the vertical wavenumber to increase, resulting in wave propagation features different from those in barotropic vortices. The stagnation radius and height are strictly constrained by the geometry of the 'critical' surface determined by the initial properties of wave-packets