This study investigated the relationship between atmospheric stratification (i.e., static stability N2 ) and vertical energy transfer of stationary planetary waves, and further illustrated the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N2 , the refractive index squared of planetary waves has a theoretical tendency to increase first and then decrease with N2 , whereas the group velocity weakens. Mechanistically, this behavior can be understood as an intensified suppression of vertical isentropic surface displacement caused by meridional heat transport of planetary waves under strong N2  conditions. Observational analysis corroborates this finding, demonstrating reduced vertical propagation velocity of waves with N2 . A linear quasi-geostrophic mid-latitude beta-plane model with constant background westerly wind and prescribed N2  applicable to the stratosphere is used to obtain analytic solutions. In this model, the planetary waves are initiated by steady energy influx from the bottom boundary. The analysis indicates that under strong N2  condition, planetary wave amplitude can be sufficiently amplified by the effective energy convergence due to the slowing vertical energy transfer, resulting in the stream function response in this model containing more energy. For the vertically quasi-linear N2 , the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.
 

planetary waves,atmospheric stratification,group velocity