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

TL;DR

This paper investigates how weak random temperature variations in a quasi-isothermal atmosphere affect acoustic-gravity waves, revealing their instability and deriving growth rates through stochastic modeling.

Contribution

It introduces a stochastic model for acoustic-gravity waves in a quasi-isothermal atmosphere with random temperature perturbations, deriving a generalized dispersion relation and instability criteria.

Findings

Acoustic-gravity waves become unstable due to random temperature inhomogeneities.

The study derives explicit instability growth rates for different noise spectra.

Random temperature fluctuations can significantly influence wave dynamics in the upper atmosphere.

Abstract

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 $\sim 200$ 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 ($\delta$-correlated in space) and the opposite case of a $\delta$-shaped noise spectrum. In both cases, instability of acoustic-gravity waves is predicted and the corresponding instability growth rates are determined.