Topological defect model of superfluid vortex filaments

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1991

OSTI ID:7041673

Carlson, N N

As a model of superfluid, the author considers a complex scalar field defined in three space dimensions which evolves in time according to a modified nonlinear Schroedinger (MNLS) equation. The equation contains a coupling to a given background flow of normal fluid. The author interprets the squared modulus of the complex scalar as the superfluid density and the phase gradient as the superfluid velocity. In a WKB type limit of the MNLS equation, obtain the superfluid Euler equation is obtained of the Landau two fluid model, modified to include the dissipative interaction with the normal fluid. Solutions of the MNLS equation may contain topological defects which are spatial zero-curves of the complex scalar with nonzero integer winding numbers. These defects are quantized superfluid vortex filaments. They persist in time and evolve as part of the overall evolution of the field. The author derives an asymptotic dynamics for the filaments from the full MNLS equation. The dynamics agrees with the common model in which the phenomenological Hall and Vinen drag force is simply added, ad hoc, to the filament dynamics of an ordinary incompressible fluid. The dynamics are complete in that precisely defined nonlocal effects are included. A special case is the dynamics of vortex filaments in the nonlinear Schroedinger equation which has the well known interpretation of vortices in an ordinary incompressible fluid. A mechanism is described by which superfluid vortices are created. It is shown that uniform flow solutions of the MNLS equation become unstable when the difference between the superfluid and normal fluid velocities becomes too large. In two space dimensions the instability leads to the spontaneous creation of vortex pairs. A numerical simulation of such a creation is presented. Also presented is a weakly nonlinear analysis of the instability. It is shown that the dynamics are governed by a perturbed Kadomtsev-Petviashvili equation.

• Research Organization: California Univ., Berkeley, CA (United States)
• OSTI ID: 7041673
• Country of Publication: United States
• Language: English

Related Subjects

665420* -- Superfluidity-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
MATHEMATICAL MODELS
MATHEMATICS
MECHANICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SUPERFLUIDITY
TOPOLOGY
VORTICES
WAVE EQUATIONS