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The three-dimensional (3D) Rossby wave energy dispersion of a tropical cyclone(TC) is studied using a baroclinic primitive equation model. The model is initialized witha symmetric vortex on a beta-plane in an environment at rest. The vortex intensifieswhile becoming asymmetric and moving northwestward due to the beta effect, and asynoptic-scale wave train forms in its wake a few of days later. The energy-dispersioninduced Rossby wave train has a noticeable baroclinic structure with alternatingcyclonic-anticyclonic-cyclonic (anticyclonic-cyclonic-anticyclonic) circulations in thelower (upper) troposphere.A key feature associated with the 3D wave train development is a downwardpropagation of the relative vorticity and kinetic energy. Due to the vertical differentialinertial stability, the upper level wave train develops faster than the lower levelcounterpart. The upper anticyclonic circulation rapidly induces an intense asymmetricoutflow jet at the southeast quadrant, and then further influences the lower-level Rossbywave train. On one hand, the outflow jet exerts an indirect effect on the lower-level wavetrain strength through changing TC intensity and structure. On the other hand, it triggersdownward energy propagation that further enhances the lower level Rossby wave train.A sudden removal of the diabatic heating may initially accelerate the energy dispersionthrough the increase of the radius of maximum wind and the reduction of the lower levelinflow. The latter may modulate the group velocity of the Rossby wave train through theDoppler shift effect. The 3D numerical results illustrate more complicated Rossby waveenergy dispersion characteristics than 2D barotropic dynamics.