VORTEX FILAMENTS, LOCAL INDUCTION AND SIMULATING
QUANTUM TURBULENCE
SCOTT STRONG
Abstract. Turbulence is an unsteady flow where vorticity, diffusion and dissipation occur on various space-time scales. Quantum effects constrain aspects
of turbulence making the superfluid case, in some sense, simpler than its classical counterpart. For such a superfluid flow the vorticity must manifest as
quantized vortex filaments and the tangling of these filaments is the hallmark
of quantum turbulence. Like the classical case, quantum turbulence is not fully
understood. However, the quantized nature of the vortex core radius is well
understood. Total concentration of vorticity to a curve is particularly appropriate for atomic Bose-Einstein condensates and superfluid Helium allowing
for aggressive analytic and numerical investigations. This talk will present
recent work exploiting this geometric constraint and, without approximation,
provides an analytic representation of the induced velocity field in terms of
elliptic integrals. Moreover, using known asymptotic representations we generalize the established local induction approximation predicting binormal flow.
Specifically, we derive a more precise proportionality constant for the binormal flow equation, which can be substituted into current superfluid simulation
techniques.
Department of Physics, Colorado School of Mines, Golden, CO 80401
E-mail address: sstrong@mines.edu
Date: January 20, 2011.
1991 Mathematics Subject Classification. 3401.
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