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Topological transition in stratified fluids

Abstract

Lamb waves are trapped acoustic-gravity waves that propagate energy over great distances along a solid boundary in density-stratified, compressible fluids1,2. They constitute useful indicators of explosions in planetary atmospheres3,4. When the density stratification exceeds a threshold, or when the impermeability condition at the boundary is relaxed, atmospheric Lamb waves suddenly disappear5. 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 the quantum valley Hall effect6,7,8 and its classical analogues9,10,11. Our study shows that the presence of Lamb-like waves encodes essential information on the underlying stratification profile in astrophysical and geophysical flows, which is often poorly constrained by observations.

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Fig. 1: Bulk dispersion relation for stratified compressible fluid.
Fig. 2: Berry curvature.
Fig. 3: Topological transition in acoustic-gravity wave spectra, depending on the sign of S.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request.

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Acknowledgements

The authors thank L.-A. Couston for help with the Dedalus code, F. Faure for providing useful insights on the index theorem, T. Alboussière, I. Baraffe, G. Chabrier, G. Laibe and M. Le Bars for their input concerning potential geophysical and astrophysical applications and L. Maas, B. Marston and N. Perez for useful comments on the manuscript. P.D. and A.V. were partly funded by ANR-18-CE30-0002-01 during this work.

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This Letter emanates from the master’s project of M.P. supervised by P.D. and A.V. All authors participated equally in the study. P.D. and A.V. wrote the manuscript.

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Correspondence to Pierre Delplace or Antoine Venaille.

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Peer review information: Nature Physics thanks Tudor Dimofte and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Information, Supplementary references 1–8.

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Perrot, M., Delplace, P. & Venaille, A. Topological transition in stratified fluids. Nat. Phys. 15, 781–784 (2019). https://doi.org/10.1038/s41567-019-0561-1

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