Vertical structure of stationary planetary waves in the presence of altitude-dependent zonal winds and dissipation

Abstract

A β plane model is formulated for the study of vertical propagation of stationary planetary waves in an atmosphere where the zonal wind, the basic state temperature field, and the Newtonian cooling coefficient are all functions of altitude. The differential equation governing a disturbance forced by a specified height field at 30 km and subject to a radiation boundary condition at great heights is solved numerically. Both the negative wind shear on the top side of the model westerly wind jet and the decrease of basic state temperature in the mesosphere are important for wave trapping of the Charney-Drazin type. Wave heat flux is the appropriate measure of wave transmission across any given level in an atmosphere where the zonal wind varies with altitude. For a weak westerly jet in which no trapping occurs the heat flux at 80 km is determined by dissipation over the path length between 30 and 80 km and is sensitive to changes in the relative position of the profiles of zonal wind and Newtonian cooling coefficient. For westerly wind jets with maximum speed of 60 m s−1 or more, characteristic of winter situations, the heat flux at 80 km is controlled by the degree of wave trapping and depends only slightly on dissipation over the path length.