Numerical study of superfluid turbulence in the self-induction approximation

Technical Report · Fri Aug 01 04:00:00 EDT 1986

OSTI ID:5132458

Buttke, T F

A numerical method is presented that determines the evolution of a superfluid vortex, and it is used to calculate some properties of turbulent superfluid vortex systems. A stable finite difference method is derived for solving the self-induction equation in vortex dynamics. The self-induction equation is equivalent to a non-linear Schroedinger equation. A numerical method is designed that preserves some of the invariants of the Schroedinger equations; this leads to stability. The method is written in terms of the tangent field of the vortex lines. It is shown that the approximate solutions exist for all times and for all initial conditions. This is the first stable numerical method for solving the self-induction equation. A new exact self-similar solution of the self-induction equation is found and this solution is used along with the previously known soliton solutions to validate the method. The method is second order accurate in space and time. The equations which govern the evolution of a superfluid vortex are viewed as a perturbation of the self-induction equation and a method is developed for determining the evolution of a superfluid vortex. The reconnection ansatz of Schwarz is incorporated into the method. The method is validated by comparison with known exact solutions and by a careful convergence check for cases where the exact solution is not known. If the spatial step in the approximation is chosen too large the approximate solutions became inaccurate. Following the work of Schwarz experiments on vortex systems are performed to find the line length density of a turbulent superfluid. The turbulence produced is not homogeneous, and line length densities and critical properties disagree with earlier results. 45 refs., 42 figs., 3 tabs.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5132458
• Report Number(s): LBL-22086; ON: DE87000926
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
SCHROEDINGER EQUATION
SOLITONS
SUPERFLUIDITY
TURBULENCE
VORTICES
WAVE EQUATIONS