Vertical Structure and Energy Transfer of Stationary Planetary Waves in Different Prescribed Atmospheric Stratification

This study investigated the relationship between atmospheric stratification (i.e., static stability N^2) and vertical energy transfer of stationary planetary waves, and further illustrated the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N^2, the refractive index squared of planetary waves has a theoretical tendency to increase first and then decrease with N^2, 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 N^2 conditions. Observational analysis corroborates this finding, demonstrating reduced vertical propagation velocity of waves with N^2. A linear quasi-geostrophic mid-latitude beta-plane model with constant background westerly wind and prescribed N^2 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 N^2 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 N^2, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.