Low-temperature decaying superfluid turbulence is studied using the nonlinear Schr\"odinger equation in the geometry of the Taylor-Green (TG) vortex flow with resolutions up to ${512}^{3}$. The rate of (irreversible) kinetic energy transfer in the superfluid TG vortex is found to be comparable to that of the viscous TG vortex. At the moment of maximum dissipation, the energy spectrum of the superflow has an inertial range compatible with Kolmogorov's scaling. Physical-space visualizations show that the vorticity dynamics of the superflow is similar to that of the viscous flow, including vortex reconnection. The implications to experiments in low-temperature helium are discussed.

Kolmogorov turbulence in low-temperature superflows

When two vortices cross, each of them breaks into two parts and exchanges part of itself for part of the other. This process, called vortex reconnection, occurs in classical and superfluids, and in magnetized plasmas and superconductors. We present the first experimental observations of reconnection between quantized vortices in superfluid helium. We do so by imaging micrometer-sized solid hydrogen particles trapped on quantized vortex cores and by inferring the occurrence of reconnection from the motions of groups of recoiling particles. We show that the distance separating particles on the just-reconnected vortex lines grows as a power law in time. The average value of the scaling exponent is approximately ½, consistent with the self-similar evolution of the vortices.

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Characterization of reconnecting vortices in superfluid helium.

Superfluid turbulence is studied using numerical simulations of the nonlinear Schrodinger equation (NLSE), which is the correct equation of motion for superflows at low temperatures. This equation depends on two parameters: the sound velocity and the coherence length. It naturally contains nonsingular quantized vortex lines. The NLSE mass, momentum, and energy conservation relations are derived in hydrodynamic form. The total energy is decomposed into an incompressible kinetic part, and other parts that correspond to acoustic excitations. The corresponding energy spectra are defined and computed numerically in the case of the two-dimensional vortex solution. A preparation method, generating initial data reproducing the vorticity dynamics of any three-dimensional flow with Clebsch representation is given and is applied to the Taylor–Green (TG) vortex. The NLSE TG vortex is studied with resolutions up to 5123. The energetics of the flow is found to be remarkably similar to that of the viscous TG vortex. The...

Decaying Kolmogorov turbulence in a model of superflow

Classical character of turbulence in a quantum liquid

The energy spectrum of superfluid turbulence is studied numerically by solving the Gross-Pitaevskii equation. We introduce the dissipation term which works only in the scale smaller than the healing length to remove short wavelength excitations which may hinder the cascade process of quantized vortices in the inertial range. The obtained energy spectrum is consistent with the Kolmogorov law.

Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with a small-scale dissipation.

The dynamical behavior of arbitrarily configured, interacting quantized vortex filaments is investigated by means of numerical experiments and analytical estimates. Several prototype situations of interest in the theory of superfluid turbulence and critical velocities are considered. It is shown that if a vortex loop approaches a surface to within a critical distance, a localized cusplike deformation is generated which drives the vortex into the surface at a well-defined point. If the vortex is reconnected to the surface in this limit, the two ends which now terminate on the surface quickly move apart. The entire process can be well approximated by making a simple reconnection at the critical distance. A similar process is found to occur when two vortex filaments try to cross, with two cusps developing which bring the lines together at a point in such a way that a line-line reconnection naturally ensues. More complicated versions of the reconnection process occur when a vortex terminates on a flat surface which contains a pinning site in the form of a local protrusion. Such a vortex is captured by the pinning site when it approaches to within a critical distance. Once a vortex is pinned, it requires a finite flow velocitymore » to free it from the pinning site. At the depinning velocity, the vortex reconnects to the flat surface and moves off. An analytical depinning criterion involving both normal and superfluid velocities is derived, and found to be in good agreement with the numerical experiments.« less

K.W. Schwarz

Papers

Three-dimensional vortex dynamics in superfluid 4He: Line-line and line-boundary interactions.