Hydrodynamics of superfluid turbulence in He II: three-dimensional theory

J.A. Geurst and H. van Beelen

Physica A: Statistical Mechanics and its Applications, 1994, vol. 206, issue 1, 58-92

Abstract: The one-dimensional hydrodynamic theory for superfluid turbulent flow of He II developed recently by one of the authors is extended to the three-dimensional case. The impulse density of the entangled mass of quantised vortices continues to play an important part in the analysis. The non-dissipative equations of motion are derived from an appropriate form of Hamilton's variational principle, while the dissipative effects are taken into account systematically according to the thermodynamics of irreversible processes. A number of helicity conservation theorems appears to be valid in the case of non-dissipative flow. Particular attention is paid to homogeneous superfluid turbulence. It turns out that the two states allowed in one-dimensional homogeneous flow, viz. the state in which the direction of the vortex tangle impulse is parallel and the one in which it is anti-parallel to the counterflow velocity, are, respectively, stable and metastable. The analysis might assist in clarifying the one-dimensional free decay of homogeneous superfluid turbulence.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:206:y:1994:i:1:p:58-92

DOI: 10.1016/0378-4371(94)90118-X

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