Numerical study of superfluid turbulence in the self-induction approximation

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1986

OSTI ID:5708093

Buttke, T F

A numerical method is presented that determines the evolution of a superfluid vortex and used to calculate some properties of turbulent superfluid vortex systems. Substantial disagreements with previous calculations are found. 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. The numerical method is designed so that it preserves some of the invariants of the Schroedinger equation; 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. A new exact self-similar solution of the self-induction equation is also found and this solution used along with the previously known soliton solutions to validate the method. It is concluded that the method is second order accurate in space and time. The equations that govern the evolution of a superfluid vortex are viewed as a perturbation of the self-induction equation, and a method for determining the evolution of a superfluid vortex is developed.

• Research Organization: California Univ., Berkeley (USA)
• OSTI ID: 5708093
• Country of Publication: United States
• Language: English

Related Subjects

640450* -- Fluid Physics-- Superfluidity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
STABILITY
SUPERFLUIDITY
TURBULENCE
VORTICES
WAVE EQUATIONS