On the propagation of oceanic waves driven by a strong macroscopic flow

TL;DR

This paper analyzes the behavior of oceanic waves influenced by strong wind forcing and rotation in a shallow water model with inhomogeneous flow, extending previous work to more complex 2D settings using advanced mathematical methods.

Contribution

It introduces an abstract semi-classical approach to diagonalize the system and identify Rossby and Poincaré waves in a 2D inhomogeneous flow, extending prior 1D analyses.

Findings

Diagonalization of the system using semi-classical methods

Dispersion relations for Poincaré waves derived via Mourre estimates

Partial results on Rossby wave propagation due to 2D complexity

Abstract

In this work we study oceanic waves in a shallow water flow subject to strong wind forcing and rotation, and linearized around a inhomogeneous (non zonal) stationary profile. This extends the study \cite{CGPS}, where the profile was assumed to be zonal only and where explicit calculations were made possible due to the 1D setting. Here the diagonalization of the system, which allows to identify Rossby and Poincar\'e waves, is proved by an abstract semi-classical approach. The dispersion of Poincar\'e waves is also obtained by a more abstract and more robust method using Mourre estimates. Only some partial results however are obtained concerning the Rossby propagation, as the two dimensional setting complicates very much the study of the dynamical system.