Discontinuities in fourth sound waves in superfluid helium

TL;DR

This paper investigates the formation and properties of fourth-sound shock waves in superfluid helium, establishing the conditions at discontinuities and highlighting differences from other sound modes.

Contribution

It introduces new physical and mathematical conditions for fourth-sound shock waves, expanding understanding of superfluid helium dynamics.

Findings

Discontinuity velocity matches fourth sound velocity

Temperature and superfluid velocity jumps are first order in pressure

Conditions differ from first- and second-sound waves

Abstract

Formation of fourth-sound shock waves in narrow channels filled with superfluid helium is studied. Physical and mathematical conditions at the surface of discontinuity are established. These conditions differ somewhat from those in case of first- and second-sound waves. The velocity of discontinuity coincides with that of fourth sound. The jumps of temperature and the superfluid velocity are shown to be of the first order as to the pressure jumps.