Coastal imbalance: generation of oceanic Kelvin waves by atmospheric perturbations

TL;DR

This paper demonstrates how atmospheric perturbations crossing a coast generate Kelvin waves in the ocean, restoring mass conservation and illustrating boundary-induced breakdown of geostrophic balance.

Contribution

It provides a linear shallow-water model analysis showing Kelvin wave generation by atmospheric perturbations at the coast, highlighting boundary effects on ocean dynamics.

Findings

Kelvin waves are generated as atmospheric perturbations cross the coast.

Generated Kelvin waves have a length scale of O(ε^{-1}) and amplitude O(ε).

Mass conservation is restored when Kelvin waves are accounted for.

Abstract

The response of a semi-infinite ocean to a slowly travelling atmospheric perturbation crossing the coast provides a simple example of the breakdown of nearly geostrophic balance induced by a boundary. We examine this response in the linear shallow-water model at small Rossby number $\varepsilon \ll 1$. Using matched asymptotics we show that a long Kelvin wave, with $O(\varepsilon^{-1})$ length scale and $O(\varepsilon)$ amplitude relative to quasigeostrophic response, is generated as the perturbation crosses the coast. Accounting for this Kelvin wave restores the conservation of mass which is violated in the quasigeostrophic approximation.