Critical Velocity and Turbulence in Superfluid Liquid Helium

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(1) Stochastic theory of vortex tangle in superfluid turbulence was developed.The extended Vinen equation for the vortex line length density and two fluid hydrodynamical equation including the generalized form of mutual friction force were obtained. Further the existence of eddy viscosity was predicted.(2) It was confirmed that some particular solutions in non-steady and non-uniform cases of Vinen equation correspond well to various turbulent patterns observed in capillary flows.(3) It was predicted that the appearance of eddy viscosity gives the interpretation of excess pressure difference observed in capillary flows as well as the interaction between boundary and vortex lines.(4) Linear instability in Couette-Taylar flow was examined on the basis of generalized two fluid hydrodynamical equations. It was shown that the result did not qualitatively agree to both magnitude and temperature dependence of the observed critical Taylar number. This result suggests that the eddy viscosity should be taken into account.(5) The possibility occuring of new condensed phase of superfluid ^3He was examined when it is put into the finite region. It was shown from variational calculation that the stabilization of B-phase is realized in place of A-phase due to size effect, and the planar state may appear under some boundary condition on the wall.(6) Superfluidity of ^4He film absorbed in the restricted geometry was intestigated. It was shown that in ^4He within zeolite the disappearance of Bose statistics leads to the decrease of transition temperature, and in^4He in Vycor glass and the sintered metallic fine particles interaction between vortex pairs becomes one dimensional and as a result agrees to the observed results qualitatively.