A microscopic approach to superfluid flow in helium2
Abstract
The vortices in superfluid helium are considered in the context of metastability of rotational flow and also through an investigation of creation of vortices in an ideal superfluid flow. The model of an ideal Bose gas initially in rotation with respect to a cylindrical container at rest having a localized roughness on the wall is considered. The solution for the time evolution of an initial state containing one, two and three vortices each of unit circulation is obtained by solving time dependent Schrodinger equation. The convergent results obtained indicate that a vortex present initially inside the container describes a trajectory which eventually reaches the cylinder wall for all ranges of values considered for a perturbation strength parameter. Once the vortex reaches the wall it disappears continuously as the node changes into a 'dimple in the wave function' which disappears continuously as a function of time. Solution of the time dependent GrossPitaevski equation, shows that a vortex present initally close to the wall moves away from it slowing down almost exponentially. So in this model of the interacting Bose gas the vortex describes a trajectory that never reaches the wall and hence corresponds to a metastable state. The vortex formation due to an effect of a protuberance from the wall bounding a semiinfinite plane is also studied.
 Publication:

Ph.D. Thesis
 Pub Date:
 1980
 Bibcode:
 1980PhDT........50K
 Keywords:

 Fluid Flow;
 Helium Isotopes;
 Liquid Helium;
 Superfluidity;
 Vortices;
 Bose Geometry;
 Metastable State;
 Perturbation Theory;
 Schroedinger Equation;
 Uniform Flow;
 Engineering (General)