Acoustic-gravity waves in quasi-isothermal atmospheres with a random vertical temperature profile

We study acoustic-gravity waves in a quasi-isothermal atmosphere in the presence of a weak random addition to the vertical temperature profile, which simulates the real atmosphere of the Earth at altitudes greater than similar to 200 km. The resulting stochastic equation is closed in the Bourret approximation. The poles of the obtained mean Green's function determine the generalized dispersion relation for acoustic-gravity waves. Two particular cases are considered: random inhomogeneities in the form of white noise (8-correlated in space) and the opposite case of a 8-shaped noise spectrum. In both cases, instability of acoustic-gravity waves is predicted and the corresponding instability growth rates are determined.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).