On the motion of a small body immersed in a two dimensional incompressible perfect fluid

TL;DR

This paper proves that as a small solid body shrinks in a 2D incompressible perfect fluid, its motion converges to a vortex-wave system influenced by a lift force akin to the Kutta-Joukowski force.

Contribution

It introduces a rigorous derivation of the vortex-wave system with lift force as the limit of shrinking bodies in ideal fluids.

Findings

Convergence of the body's motion to a vortex-wave system

Identification of a lift force similar to Kutta-Joukowski in the limit

Extension of vortex dynamics theory to shrinking solid bodies

Abstract

In this paper we prove that the motion of a solid body in a two dimensional incompressible perfect fluid converges, when the body shrinks to a point with fixed mass and circulation, to a variant of the vortex-wave system where the vortex, placed in the point occupied by the shrunk body, is accelerated by a lift force similar to the Kutta-Joukowski force of the irrotational theory.