Scattering of first and second sound waves by quantum vorticity in superfluid Helium

TL;DR

This paper investigates how quantum vortices in superfluid helium scatter and convert first and second sound waves, providing explicit formulas and analyzing the conversion efficiencies through a vortex dipole example.

Contribution

It offers a detailed analysis of sound wave scattering by quantum vorticity, including explicit expressions and validity conditions within a two-fluid hydrodynamics framework.

Findings

Most incident first sound converts into second sound.

Second sound partly converts into first sound.

Explicit formulas for scattered pressure and temperature are derived.

Abstract

We study the scattering of first and second sound waves by quantum vorticity in superfluid Helium using two-fluid hydrodynamics. The vorticity of the superfluid component and the sound interact because of the nonlinear character of these equations. Explicit expressions for the scattered pressure and temperature are worked out in a first Born approximation, and care is exercised in delimiting the range of validity of the assumptions needed for this approximation to hold. An incident second sound wave will partly convert into first sound, and an incident first sound wave will partly convert into second sound. General considerations show that most incident first sound converts into second sound, but not the other way around. These considerations are validated using a vortex dipole as an explicitely worked out example.