Vertical propagation of planetary rossby waves through an atmosphere with Newtonian cooling

Abstract

A linearized model for the vertical propagation of Rossby waves through an atmosphere with Newtonian cooling is derived. The nature of the vertical propagation depends on the time scale for Newtonian cooling and for horizontal advection by a mean wind, various approximate models being defined according to the relative magnitude of these two time scales. A solution is obtained for the vertical propagation of stationary Rossby waves with Newtonian cooling through a constant mean wind atmosphere. Such waves are highly attenuated for very weak westerly mean winds and are least attenuated for westerly winds of strength somewhat below the propagation cutoff velocity. This attenuation greatly reduces the possible upward vertical propagation of planetary waves through the terrestrial atmosphere near the equinoxes and is quantitatively significant throughout the winter.