Representation of equatorial waves by a single scalar field and the effect of the horizontal component of the Earth's rotation

TL;DR

This paper introduces a new scalar field representation for equatorial waves to analyze how the often-neglected horizontal component of Earth's rotation affects wave dispersion, showing it has no impact when the Brunt-Väisälä frequency is constant.

Contribution

It presents a novel scalar field approach to equatorial waves and demonstrates the horizontal Earth's rotation component's effect on wave dispersion.

Findings

Horizontal component of Earth's rotation has no effect on dispersion with constant N.

New scalar field simplifies equatorial wave analysis.

Dispersion relation remains unchanged with horizontal rotation component for constant N.

Abstract

A new representation for equatorial waves in terms of a single scalar field is used to demonstrate the influence of the (usually neglected) horizontal component of the earth's rotation vector $\boldsymbol{\vec\Omega}$ on the dispersion of the waves. It is shown that, in the case of constant Brunt-V\"ais\"al\"a frequency $N$, the dispersion relation is unaltered when the horizontal component of $\boldsymbol{\vec\Omega}$ is included.