Point Vortex Dynamics on Closed Surfaces
Master Thesis at TU Berlin (2018). Supervision: Ulrich Pinkall
Point vortices moving on a plane (left), a sphere (middle), and a bunny (right).
Abstract
The theory of point vortex dynamics has existed since Kirchhoff's proposal in 1891 and is still under development with connections to many fields in mathematics. As a strong simplification of the concept of vorticity it excels in computational speed for vorticity-based fluid simulations at the cost of accuracy. Recent findings by Stefanella Boatto and Jair Koiller allowed the extension of this theory onto closed surfaces. This thesis presents a comprehensive guide to point vortex dynamics on closed surfaces with genus zero and vanishing total vorticity, unifying the theory for the plane, the sphere, and closed surfaces, along with implementation details and supplemental material.
Talk
BibTeX
@article{padilla2018pointvortices,
author = {Marcel Padilla},
title = {Point Vortex Dynamics on Closed Surfaces},
journal = {M.S. Thesis},
year = {2018},
month = {05},
publisher = {TU Berlin},
}