Geometric phases of water waves

TL;DR

This paper explores the geometric phases of water waves, linking crest slowdown phenomena to geometric and dynamical phase velocities, supported by theoretical predictions and ocean field observations.

Contribution

It introduces a novel geometric phase framework for understanding water wave crest slowdown, connecting wave dynamics to principal fiber bundle theory.

Findings

Theoretical predictions align with ocean observations.

Average crest speed is approximately 80% of the phase velocity.

Geometric and dynamical phases influence wave crest speeds.

Abstract

Recently, Banner et al. (2014) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrowband waves, this is related to the geometric and dynamical phase velocities $U_d$ and $U_g$ associated with the parallel transport through the principal fiber bundle of the wave motion with $\mathit{U}(1)$ symmetry. The theoretical predictions are shown to be in fair agreement with ocean field observations, from which the average crest speed $c=U_d+U_g$ with $c/U_d\approx0.8$ and $U_{g}/U_d\approx-0.2$.