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

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.