The Vertical Propagation of Forced Atmospheric Planetary Waves

Abstract

Adiabatic, inviscid, quasi-geostrophic perturbations on a β plane are forced at some initial time by the switch-on of a vertical velocity or temperature disturbance at the base of a stratified atmosphere. The vertical variation of the basic zonal wind is represented by three simple layered models. A Laplace-transformed potential yorticity equation is solved in each layer, and after solutions are matched across interfaces, inversion integrals are evaluated numerically and asymptotically. After initial high-frequency planetary waves have died out by radiating energy to infinity, the response primarily consists of a standing-wave mode and a traveling barotropic Rossby mode. In spite of the fact that the barotropic model propagates energy vertically with an infinite group velocity, a signfficant build-up of wave energy is not realized until many days after the switch-on. The time dependence of energy and heat fluxes is caused by the interaction of these modes. The role of unstable modes and other vertically propagating groups of planetary waves is considered. The propagation of energy into the upper atmosphere is shown to be strongly affected by the presence of westerly wind maxima where the speed exceeds the critical value for propagation of energy by stationary planetary waves. Delays in the arrival of energy by a day or more can be caused by such regions.