Shohei Kashiwamura

Stochastic theory of vortex tangle in superfluid turbulence

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.

Three-Fluid Hydrodynamics for Vortex Turbulence in Superfluid 4He

Two-fluid hydrodynamics is extended to three-fluid hydrodynamics including the “vortex fluid”, which denotes the system of vortex lines with the inertia mass of the vortex core. Characteristic cons...

An approach to dynamical description of dissipative systems

Abstract A general framework for dynamical description of dissipative systems in classical physics is presented. Making use of the interaction representation and a projection operator we derive a dynamical equation of probability distribution functions. Then the variational method accompanying the mirror image field is investigated in connection with the derivation of the Fokker-Planck equation and specifically the Ornstein-Uhlenbeck process. To enlighten the situation with respect to the variational method for dissipative systems, the least principle of dissipation energy proposed by Onsager and Machlup is examined. The relation between these two approaches is clarified in the light of stochastic processes.

Effects of eddy viscosity of turbulent superfluid in capillary flows

Abstract Effects of “eddy viscosity” on superfluid turbulence associated with the vortex tangle are discussed in terms of the interpretation of pressure difference in various types of capillary flow and also in regard to the velocity profiles of normal- and superfluid over the capillary cross section. The eddy viscosity coefficient and the boundary value of superfluid velocity on the capillary wall are treated as parameters that are determined by fitting to the observed data of pressure differences in the pure superflow and thermal counter flow. Using these parameters, it is shown that in the well-developed turbulent state the relative velocity between the normal fluid and the superfluid shows almost uniform profile over the cross section of the capillary except very near the boundary wall. This situation partially supports recent successful analysis of temperature difference, which relied on the dynamical scaling theory in the assumed homogeneous velocity fields and distributions for the vortex tangle.

Kinetic theory of mutual friction force in superfluid 4He with vortex lines

Abstract Derivation of the mutual friction force between normal fluid and superfluid flows mediated by vortex lines is formulated on the basis of the kinetic theory for quasiparticle gas (phonons and rotons), in the case where two-fluid hydrodynamics is valid. Correspondence with the phenomenological theory is shown unambiguously, with respect to the issue about the Iordanskii force, the origin of the force on the vortex line due to quasiparticles, and the force balance relation between the Magnus force and the force from the normal fluid.