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

This study investigates the relationship between atmospheric stratification (i.e., static stability given by $ {N}^{2} $) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric $ {N}^{2} $, the refractive index square of planetary waves has a theoretical tendency to increase first and then decrease with an increased $ {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 a reduction in the vertical-propagation velocity of waves with increased $ {N}^{2} $. A linear, quasi-geostrophic, mid-latitude beta-plane model with a constant background westerly wind and a 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 lower boundary. The analysis indicates that under strong $ {N}^{2} $ conditions, the amplitude of planetary waves can be sufficiently increased by the effective energy convergence due to the slowing vertical energy transfer, resulting in a streamfunction response in this model that contains more energy. For $ {N}^{2} $ with a quasi-linear vertical variation, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.