Manifestation of the Berry curvature in geophysical ray tracing

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