Global singularity-free solution of the Iordanskii force problem

TL;DR

This paper derives a singularity-free, comprehensive solution for the transverse force on a hydrodynamic vortex caused by sound waves, resolving previous contradictions in the literature.

Contribution

It provides the first global, singularity-free derivation of the Iordanskii force using matched asymptotic expansions, clarifying the vortex-wave interaction.

Findings

The solution eliminates singularities in the momentum exchange.

It offers a consistent calculation of the transverse force.

Resolves longstanding contradictions in the theoretical understanding.

Abstract

We present a derivation of the transverse force acting on a hydrodynamic vortex in the presence of an incoming sound wave from a global solution of the scattering problem, using the method of matched asymptotic expansions. The solution presented includes a detailed treatment of the interaction of the incident wave with the vortex core, and is free from the singularities in the momentum exchange between vortex and sound wave which have led to contradictory results for the value of the transverse force in the literature.