Influence of temperature-dependent density inhomogeneity on the stability of atmospheric stratified fluids

The stability of atmospheric stratified fluids is revisited to study the influence of the temperature-dependent density inhomogeneity due to thermal expansion in the Earth's lower atmosphere (with heights $0$ to $50$ km) under the action of gravity. Previous theory in the literature [Phys. Lett. A 480 (2023) 128990] is modified and advanced. It is found that the Brunt-V{\"a}is{\"a}l{\"a} frequency associated with internal gravity waves is modified, leading to new instability conditions of vertically stratified fluids. The possibility of the onset of Rayleigh-B{\'e}nard convective instability is also discussed, and the influences of the modified Brunt-V{\"a}is{\"a}l{\"a} frequency and the density and temperature gradients on the instability growth rates are studied.