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On the hydrodynamic equations for flow of liquid helium II with mutual friction

Published online by Cambridge University Press:  28 March 2006

A. A. Townsend
A. A. Townsend
Affiliation:
Emmanuel College, Cambridge
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Abstract

The flow of liquid helium II at subcritical velocities can be described by hydrodynamic equations which assume the possibility of independent motions of the two fluid components, but difficulties arise in supercritical flows with forces of mutual friction between the component fluids. The extensive evidence that mutual friction is caused by scattering of the thermal excitations in the velocity fields of the quantized vortex lines suggests that the equations should include mutual forces which are large near the vortex-lines and negligible elsewhere. In their original theory, Hall & Vinen (1956) did assume this, and here the implications of the assumption are examined in detail. Serious difficulties are found in reconciling localization of the mutual friction with fully developed flow in channels, and it is suggested that, although the mutual friction arises from scattering near the vortex lines, the force on the superfluid is distributed uniformly over distances comparable with the distance between adjacent vortex lines.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 15 , Issue 2 , February 1963 , pp. 262 - 272
Copyright
© 1963 Cambridge University Press

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References

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Townsend, A. A. 1961 J. Fluid Mech. 10, 113.
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