Equatorial wind-drift currents with a continuous stratification and centripetal effects in the $\beta$-plane setting

TL;DR

This paper derives an exact steady solution for three-dimensional wind-driven equatorial currents considering stratification and centripetal effects within the $eta$-plane approximation, enhancing understanding of equatorial flow dynamics.

Contribution

It provides a novel explicit analytical solution for stratified equatorial flows with centripetal effects, which was not previously available.

Findings

The thermocline shows monotonicity properties.

The solution models the equatorial current with a flat surface and bed.

The approach uses functional analysis to analyze flow properties.

Abstract

In this paper, we aim to derive an exact solution to the three-dimensional governing equations for wind-induced equatorial flows in the $\beta$-plane approximation with a depth-dependent density distribution and subjected to centripetal terms. The obtained explicit solution represents a steady purely azimuthal stratified flow with a flat surface and an impermeable flat bed that is suitable for describing the Equatorial Current. Resorting to a functional analysis, we show that the thermocline exhibits some monotonicity properties.