Manifestation of Berry curvature in geophysical ray tracing

TL;DR

This paper demonstrates how Berry curvature influences geophysical wave ray tracing, revealing new effects on wave propagation and polarization, especially in shallow water waves and mid-latitude phenomena.

Contribution

It introduces a variational WKB method to incorporate Berry curvature into geophysical ray tracing, providing a novel geometric perspective on wave propagation.

Findings

Berry curvature affects wave ray trajectories in geophysical fluids.

Predicted larger eastward velocity for Poincaré wave packets.

New interpretation of equatorial oscillation and ray bending in mid-latitudes.

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 Berry curvature, describing the local geometry of wave polarization relations and known to appear in the equations of motion of multi-component wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atoms physics. Here, we use a variational method with a vectorial Wentzel-Kramers-Brillouin (WKB) ansatz to derive ray tracing equations in geophysical waves and reveal the contribution of Berry curvature. We detail the case of shallow water wave packets and propose a new interpretation to the equatorial oscillation and the bending of rays in mid-latitude area. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for Poincar\'e wave packets. This work enlightens the role of wave polarization's geometry in various geophysical and astrophysical fluid waves, beyond the shallow water model.