Semiclassical and spectral analysis of oceanic waves

TL;DR

This paper analyzes oceanic waves using semiclassical and spectral methods, showing Rossby waves form closed trajectories under certain conditions while Poincaré waves disperse, revealing different long-term behaviors.

Contribution

It introduces a combined semiclassical and spectral framework to study the long-term dynamics of Rossby and Poincaré waves in oceanic flows.

Findings

Rossby waves form closed trajectories over time

Poincaré waves disperse at large times

Different spectral behaviors for Rossby and Poincaré waves

Abstract

In this work we prove that the shallow water flow, subject to strong wind forcing and linearized around an adequate stationary profile, develops for large times closed trajectories due to the propagation of Rossby waves, while Poincar\'e waves are shown to disperse. The methods used in this paper involve semi-classical analysis and dynamical systems for the study of Rossby waves, while some refined spectral analysis is required for the study of Poincar\'e waves, due to the large time scale involved which is of diffractive type.