Stratified equatorial flows in cylindrical coordinates with surface tension

TL;DR

This paper models steady, large-scale equatorial flows of an inviscid, incompressible fluid with surface tension in cylindrical coordinates, analyzing the effects of gravity and surface tension on free surface dynamics.

Contribution

It introduces a mathematical model for steady equatorial flows with surface tension in cylindrical coordinates and proves a regularity result for the free surface.

Findings

Derived a model for steady equatorial flows with surface tension

Proved a regularity result for the free surface

Analyzed the effects of gravity and surface tension on flow dynamics

Abstract

This paper considers a mathematical model of steady flows of an inviscid and incompressible fluid moving in the azimuthal direction. The water density varies with depth and the waves are propagating under the force of gravity, over a flat bed and with a free surface, on which acts a force of surface tension. Our solution pertains to large scale equatorial dynamics of a fluid with free surface expressed in cylindrical coordinates. We also prove a regularity result for the free surface.