The interplay of curvature and vortices in flow on curved surfaces

TL;DR

This paper investigates how the geometry and topology of curved surfaces influence fluid flow and vortex behavior, using numerical methods to demonstrate flow manipulation through geometric changes.

Contribution

It introduces a surface vorticity-stream function formulation solved via parametric finite elements to study vortex dynamics on curved surfaces, highlighting geometric control of flow.

Findings

Geometry affects vortex placement and flow patterns.

Flow can be manipulated by changing surface geometry.

Numerical examples demonstrate flow control via geometric modifications.

Abstract

Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements. Motivated by designed examples for superfluids, we consider the influence of a geometric potential on vortices for fluids with finite viscosity and show numerical examples in which a change in the geometry is used to manipulate the flow field.