Abstract
Stochastic theory of vortex tangle turbulence in superfluid 4He is reformulated to extend Schwarz theory to spatially inhomogeneous case. Starting with the equation of motion for superfluid velocity under an arrangement of vortex tangle, the equation of motion for the vortex line element is described by a Langevin type equation and Fokker-Planck type equation is derived for the distribution function of vortex line length. Assuming a scaling hypothesis of velocity and an universal property of the distribution function, the extended formula of Vinen- Schwarz equation is derived. By taking the average of starting equation over stochastic process, the hydrodynamical equation for the superfluid velocity can be written in a form with the mutual friction force and “eddy viscosity” term.
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