Abstract
A stochastic theory for the dynamics of vortex tangle in superfluid turbulence is developed along the theory of Brownian motion in a form involving the spatially inhomogeneous case of vortex distribution. The motion of the vortex line is expressed, taking account of its random character, by the Langevian equation for position and velocity of the line core. On this basis the Fokker-Planck type equation for the local distribution function of the vortex line length is derived, and then assuming the scaling property of the distribution function, the extended Vinen-Schwarz equation for the line length density is derived. By taking the stochastic average of the equation of motion for superfluid velocity, its hydrodynamical equation is given in a form associated with not only the mutual friction force, but also a possible term leading to the “eddy” viscosity. A problem on the entropy production due to the vortex tangle is further discussed in comparison with the phenomenological hydrodynamic formulation.
Published Version
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