Stratified equatorial flows in cylindrical coordinates with surface tension

2025/05/14 by Cristina Gheorghe, Gheorghe, Cristina, Andrei Stan +1
Mathematics · Earth and Planetary Sciences · Engineering · #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #Fluid dynamics and aerodynamics studies

paper · doi:10.48550/arxiv.2506.08016

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.

Citations

• On the analyticity of periodic gravity water waves with integrable vorticity function
• An exact solution for equatorially trapped waves
• Doubling properties for second order parabolic equations
• On the exponential solution of differential equations for a linear operator

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