CE30 - Physique de la matière condensée et de la matière diluée

Wave Topology in Fluids – WTF

Wave Topology in Fluids (WTF)

The concept of topological wave was initially developped in the context of the quantum Hall effect. It has experienced unprecedented growth in most areas of physics in recent years. However, until our first work in 2017, these ideas had never been applied to fluids. Our project aims to establish the foundations of wave topology in fluids, from microfluidics to planetary and astrophysical flows.

Foundation of Wave Topology in Fluids

The aim is to provide the first experimental demonstrations of topological phases in liquids, to demonstrate their ubiquity in geophysical and astrophysical flows, to explain the emergence of new topological waves in the absence of edges in a physical system, and to find other manifestations of topology in fluids.

-Theory: bulk-edge correspondence, scattering, ray tracing, ...
-Numerics: simulations of linear and nonlinear fluid dynamics.
-Laboratory experiments: active liquids.

-Discovery of «topological« waves in compressible stratified fluids, with a prediction of observations in astro-seismology (Nat. Phys. 2019).

-Demonstration of a new phase of active liquids (Experiment and theory): A vortex glass base. While liquids are capable of stationary flow at constant speed, their flows never relate their singularities which form a glass of topological defects (preprint).

-Demonstration of the propagation of topologically protected waves along non-orientable surfaces, such as elastic ribbons or soap films in the form of Moebius ribbons (Phys Rev X 2019).

-Generalization of edge-volume correspondence to continuous media (JFM 2019, Phys. Rev. Res. 2020) to disordered chiral topological phases (preprint).


-Manifestation of Berry curvaature in astro/geo-physical ray tracing (in progress).

- Our experiments on active matter liquids have made it possible to achieve stable flows which should make it possible to probe the topological phases of the waves propagating there (in progress).

-Application of topology tools to coastal waves in oceanography (in progress).

-Effect of disorder, dissipation and nonlinearities on topological fluid waves

Perrot, M., Delplace, P., & Venaille, A. (2019). Topological transition in stratified fluids. Nature Physics, 15(8), 781-784.

Bartolo, D., & Carpentier, D. (2019). Topological Elasticity of Nonorientable Ribbons. Physical Review X, 9(4), 041058.

Tauber, C., Delplace, P., & Venaille, A. (2019). A bulk-interface correspondence for equatorial waves. Journal of Fluid Mechanics, 868, R2.

Tauber, C., Delplace, P., & Venaille, A. (2020). Anomalous bulk-edge correspondence in continuous media. Physical Review Research, 2(1), 013147.

Delplace, P., & Venaille, A. (2020). From the geometry of Foucault pendulum to the topology of planetary waves. arXiv preprint arXiv:2006.08488. Accepté
pour CRAS, Compte rendus Physique

Guzmán, M., Bartolo, D., & Carpentier, D. (2020). Geometry and Topology Tango in Chiral Materials. arXiv preprint arXiv:2002.02850.

Chardac, A., Shankar, S., Marchetti, M. C., & Bartolo, D. (2020). Meandering flows and dynamical vortex glasses in disordered polar active matter. arXiv preprint arXiv:2002.12893.

The concept of topologically-protected transport along the edge of physical systems was born three decades ago in the context of quantum Hall electronics. A second topological revolution has occurred over the last ten years, when physicists realized that topological protection applies to virtually all areas of physics, from photonics to mechanics. Waves are protected from disorder and backscattering when propagating at the boundary separating materials with different topological properties. This year we showed that these ideas can be used to account for robust transport in fluids, from microfluidics to geophysical scales. Building on these pioneering results we ambition to lay out the foundation of Wave Topology in Fluids. We will provide the first experimental evidence of topologically protected waves in liquids, we will demonstrate their ubiquity in geophysical and astrophysical flows, and we will explain the emergence of novel topological waves in the absence of physical boundaries.

Project coordinator


The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.



Help of the ANR 471,468 euros
Beginning and duration of the scientific project: March 2019 - 48 Months

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