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

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  • Geurst, J.A.
  • van Beelen, H.

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.

Suggested Citation

  • Geurst, J.A. & van Beelen, H., 1994. "Hydrodynamics of superfluid turbulence in He II: three-dimensional theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(1), pages 58-92.
    • Handle: RePEc:eee:phsmap:v:206:y:1994:i:1:p:58-92
    DOI: 10.1016/0378-4371(94)90118-X
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    Cited by:

    1. Geurst, J.A. & van Beelen, H., 1995. "Hydrodynamics of superfluid turbulence fronts in He II: steady propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(4), pages 407-434.

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