G- and p-mode oscillations in Earth’s atmosphere are mathematically possible

In helioseismology – and in asteroseismology, more generally – g- and p-mode oscillations are known types of surface fluid oscillations restored by buoyancy and pressure, respectively. By applying small perturbations to the Euler equations describing the Earth’s atmosphere, Tetu Makino aimed to show these types of oscillations can also exist on the planet surface.

Makino found that g- and p-mode oscillations can both occur in Earth’s atmosphere under very specific conditions. For sufficiently small but nonzero frequencies of the perturbation, there can be at least one eigenvalue that approaches zero, which satisfies the buoyancy requirement for the existence of g-modes, and at least one eigenvalue approaching infinity, satisfying the requirement for p-modes. To confirm these are not simply mathematical byproducts, he also ensured the presence of nonzero eigenvalues.

“Although astrophysicists know g-modes well, meteorologists seem to scarcely pay attention to g-mode oscillations,” said Makino. “I hope some interesting implications of the g-mode oscillations will be found in meteorological researches.”

He considered this problem on a background stratified atmosphere, which touches the vacuum of space at a finite height of the stratosphere. Various types of potential perturbations were compared to determine the feasible conditions for achieving the desired oscillations.

For mathematical simplicity, Makino neglected the curvature and rotation of the Earth, though he notes that future analyses should take these parameters into account to obtain a more complete description of Earth’s atmospheric oscillations.

“I hope I will be able to see more and more beautiful landscapes in the mathematically rigorous cases,” he said.

Source: “On adiabatic oscillations of a stratified atmosphere on the flat earth,” by Tetu Makino, Journal of Mathematical Physics (2020). The article can be accessed at https://doi.org/10.1063/5.0014743 .