Manifestation of the Berry curvature in geophysical ray tracing
Abstract
Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named the Berry curvature, which describes the local geometry of wave polarization relations and is known to appear in the equations of motion of multicomponent wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atom physics. Here, we use a variational method with a vectorial WentzelKramersBrillouin ansatz to derive ray tracing equations for geophysical waves and to reveal the contribution of the Berry curvature. We detail the case of shallowwater wave packets and propose a new interpretation of their oscillating motion around the equator. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for Poincaré wave packets. This work enlightens the role of the geometry of wave polarization in various geophysical and astrophysical fluid waves, beyond the shallowwater model.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 April 2021
 DOI:
 10.1098/rspa.2020.0844
 arXiv:
 arXiv:2010.05575
 Bibcode:
 2021RSPSA.47700844P
 Keywords:

 Physics  Fluid Dynamics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Physics  Atmospheric and Oceanic Physics
 EPrint:
 20 pages, 4 figures