Evanescent acoustic-gravity waves in a rotating stratified atmosphere

Abstract

In this work, we focused on the study of the influence of the rotation of the Earth’s atmosphere on the properties of evanescent acoustic-gravity waves, which we studied earlier in the absence of rotation. It is shown that evanescent acoustic-gravity waves (AGW) with a continuous spectrum can exist in an atmosphere rotating with an angular frequency Ω below the frequency 2 Ω (the Coriolis parameter). It is also shown that the rotation of the atmosphere also leads to a modification of the previously discovered continuous spectrum of evanescent AGWs with frequencies higher than the Coriolis parameter, which fills the entire “forbidden” region in the diagnostic diagram between freely propagating acoustic and internal gravity waves. It is concluded that the AGW spectrum in the diagnostic diagram consists of regions of acoustic and gravity waves, as well as two regions of evanescent waves, and is continuous. The found new spectrum expands the full spectrum of evanescent waves and indicates the need to search for evanescent waves at ultra-low frequencies. The result is obtained for high-latitude regions from a system of linear hydrodynamic equations for perturbations that take into account the rotation of the Earth’s atmosphere, by imposing an additional spatial relation on the components of the perturbed velocity vector of the elementary volume of the medium, which proposed by us for the first time. This made it possible to obtain an infinite number of solutions describing evanescent acoustic-gravity waves propagating in an isothermal atmosphere. The specified connection between the components of the perturbed velocity is characterized by the α parameter, which can only take real values. It has been established that the detected spectrum of evanescent acoustic-gravity waves can exist only at 0 < α < 1 , while the previously found spectrum of these waves, modified by taking into account the Earth’s rotation, is realized at arbitrary values of α . Analytical and numerical analysis of the obtained solutions is carried out. It is shown that these solutions, at certain values of the parameter α , pass into the previously studied evanescent modes.