Topological transition in stratified fluids

TL;DR

This paper uses topological physics to predict new Lamb-like waves in stratified fluids, revealing how wave existence relates to stratification profiles and symmetry properties, with implications for astrophysical and geophysical observations.

Contribution

It introduces a topological framework to identify Lamb-like waves in stratified fluids without solid boundaries, linking wave existence to band crossings and symmetry restoration.

Findings

Lamb-like waves are predicted to exist based on topological band crossing points.

Wave existence depends on stratification profile and symmetry conditions.

These waves encode information about the stratification in astrophysical and geophysical flows.

Abstract

Lamb waves are trapped acoustic-gravity waves that propagate energy over great distances along a solid boundary in density stratified, compressible fluids. They constitute useful indicators of explosions in planetary atmospheres. When the density stratification exceeds a threshold, or when the impermeability condition at the boundary is relaxed, atmospheric Lamb waves suddenly disappear. Here we use topological arguments to predict the possible existence of new trapped Lamb-like waves in the absence of a solid boundary, depending on the stratification profile. The topological origin of the Lamb-like waves is emphasized by relating their existence to two-band crossing points carrying opposite Chern numbers. The existence of these band crossings coincides with a restoration of the vertical mirror symmetry that is in general broken by gravity. From this perspective, Lamb-like waves also bear strong similarities with boundary modes encountered in quantum valley Hall effect. Our study shows that the presence of Lamb-like waves encode essential information on the underlying stratification profile in astrophysical and geophysical flows, which is often poorly constrained by observations.