A number theoretical observation of a resonant interaction of Rossby waves

TL;DR

This paper explores the resonant interactions of Rossby waves using number theory, revealing unique frequency clusters and the absence of horizontal-axis resonances, advancing understanding of geophysical wave dynamics.

Contribution

It introduces a novel number theoretical approach to analyze Rossby wave resonances, identifying specific frequency clusters and their properties.

Findings

Resonant frequencies form distinct clusters.

No resonant frequencies occur on the horizontal axis.

Number theory provides new insights into wave interactions.

Abstract

Rossby waves are generally expected to dominate the $\beta$ plane dynamics in geophysics, and here in this paper we give a number theoretical observation of the resonant interaction with a Diophantine equation. The set of resonant frequencies does not have any frequency on the horizontal axis. We also give several clusters of resonant frequencies.