Geometric, Stochastic and Algebraic Vortices

Abstract

Mathematical concepts can often be understood in one of three complementary ways: geometric, algebraic or stochastic. In this chapter I show how vortices may be interpreted in each of these three ways. Each point of view is appropriate for certain applications, and each sheds new light on the role played by vortices in fluid dynamics. This review is necessarily brief, and makes no attempt to be exhaustive, but I hope it gives an interesting overview of vortices in all their forms.