Algebraic spiral solutions of 2d incompressible Euler

TL;DR

This paper constructs a class of self-similar solutions to the 2D incompressible Euler equations where vorticity forms algebraic spirals near the origin, providing insight into vortex sheet roll-up behavior.

Contribution

It introduces a novel class of algebraic spiral solutions for the 2D Euler equations, expanding understanding of vortex dynamics and self-similar flow structures.

Findings

Vorticity forms algebraic spirals near the origin.

Solutions exhibit self-similarity in the flow.

Provides a mathematical framework for vortex sheet roll-up.

Abstract

We consider self-similar solutions of the 2d incompressible Euler equations. We construct a class of solutions with vorticity forming algebraic spirals near the origin, in analogy to vortex sheets rolling up into algebraic spirals.