Resonant oscillations of intermediate frequency in a stratified atmosphere

Abstract

A class of solutions to a model of forced oscillations in a rotating stratified atmospheric layer is derived and analyzed. The present study corresponds to the tropospheric response to dynamic forcing with frequency between an inertial value, associated with the earth's rotation, and the frequency of an adiabatic oscillation (Brunt-Väisälä frequency). The basic model is found to reduce to a boundary value problem with a second-order linear partial differential equation of the hyperbolic type for this range of forcing frequencies. The forced solutions are shown to exhibit resonances with the normal modes of oscillation of the layer. The characteristics of the resonant modes are analyzed in terms of mean tropospheric values of temperature, temperature lapse, wind speed, horizontal and vertical wind shears, latitude, and the frequency and horizontal wavelength of the forcing mechanism. These solutions are compared with solutions to the model for a different (subinertial) range of forcing frequencies; this comparison leads to an elliptic boundary value problem. The solutions in that case do not exhibit the same type of resonance and generally decay away from the region of forcing. Selected results of resonant oscillations for a diurnal frequency of forcing are given and yield insight into the manner by which diurnal thermal forcing near the earth's surface can dynamically influence the wind and temperature field in the middle and upper troposphere.