Splitting of the Wave Disturbance Spectrum in the Isothermal Atmosphere Due to Its Rotation

Abstract

The influence of the Earth’s rotation on the spectrum of low-frequency wave disturbances in an isothermal atmosphere is investigated. The system of equations for small linear disturbances is obtained in the “traditional” approximation and in the β-plane approximation, taking into account the frequency of rotation of the atmosphere. The found equations differ from the previously obtained ones in that the left parts of the equations depend only on time, whereas the right parts are expressed in terms of disturbed pressure. It is shown that, at zero perturbed pressure, taking into account the atmospheric rotation in the equations leads to the “splitting” of the obtained system into separate equations describing vertical and horizontal perturbations. Compact analytical solutions were obtained for both types of disturbances. It was established that vertical disturbances are realized in the form of Brunt–Väisälä waves, while horizontal are realized in the form of Rossby waves and inertial oscillations.