Free-surface equatorial flows with surface tension in spherical coordinates
Andrei Stan
TL;DR
This paper derives an exact analytical solution for steady, azimuthal equatorial flows with free surfaces and surface tension in spherical coordinates, revealing how pressure variations determine free surface shape.
Contribution
It provides a novel exact solution for free-surface equatorial flows with surface tension in spherical coordinates, linking pressure variations to free surface shape.
Findings
Exact solution for steady azimuthal flow in spherical coordinates
Pressure variations uniquely determine free surface shape
Analytic techniques applied to free surface boundary conditions
Abstract
In this paper, we determine an exact solution to the governing equations in spherical coordinates for an inviscid, incompressible fluid. This solution describes a steady, purely azimuthal equatorial flow with an associated free surface. Using functional analytic techniques, we demonstrate that if a free surface is known beforehand, the variations in pressure needed to achieve this surface implicitly define the shape of the free surface in a unique way.
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Taxonomy
TopicsAquatic and Environmental Studies · Fluid dynamics and aerodynamics studies · Fluid Dynamics and Heat Transfer