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Discontinuities in helium II

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Abstract

The jump conditions at surface of discontinuity are derived for the two-fluid model of helium II from postulated balance laws for the total energy, the linear momentum of the superfluid and from an entropy production inequality. These conditions are used to discuss a contact surface and the propagation of a weak shock.

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Abbreviations

A :

Helmholtz free energy function (A=U−ST)

F s i :

external body force acting on the superfluid

f s i :

superfluid acceleration (=∂ t v s i +v s k u s i,k )

G s i :

density of supply of linear momentum to the superfluid

g s i :

diffusive force of the superfluid (=G s i −m s v s i )

m s :

short notation for ∂ t ρs+(ρs v s k ), k

qk :

heat flux vector per unit area per unit time

r :

heat supply function per unit mass unit per time

S :

entropy per unit mass of helium II

T :

absolute temperature (> 0)

t s i :

superfluid stress vector ( s i =n k σ s ki )

U :

internal energy per unit mass of helium II

v s i :

superfluid velocity

ρ :

total mass density

ρ s :

superfluid mass density

σ s ij :

superfluid stress tensor

References

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland UK

    R. N. Hills

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  1. R. N. Hills
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Hills, R.N. Discontinuities in helium II. Appl. Sci. Res. 27, 145–155 (1973). https://doi.org/10.1007/BF00382484

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  • DOI: https://doi.org/10.1007/BF00382484

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