HYDRODYNAMICS OF SUPERFLUID TURBULENCE IN HE-II - 3-DIMENSIONAL THEORY

The one-dimensional hydrodynamic theory for superfluid turbulent flow of He II developed recently by one of the authors is extended to the t hree-dimensional case. The impulse density of the entangled mass of qu antised vortices continues to play an important part in the analysis. The non-dissipative equations of motion are derived from an appropriat e form of Hamilton's variational principle, while the dissipative effe cts are taken into account systematically according to the thermodynam ics of irreversible processes. A number of helicity conservation theor ems appears to be valid in the case of non-dissipative flow. Particula r 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 para llel and the one in which it is anti-parallel to the counterflow veloc ity, are, respectively, stable and metastable. The analysis might assi st in clarifying the one-dimensional free decay of homogeneous superfl uid turbulence.