  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.

Fluid Dynamics;Mesoscale and Nanoscale Physics;Atmospheric and Oceanic Physics