Statistical laws and self-similarity of vortex rings emitted from a localized vortex tangle in superfluid ${}^4$He

Abstract

We numerically simulated quantum turbulence in superfluid ${}^4$He to investigate the emission of vortex rings from a localized vortex tangle. Turbulence is characterized by some universal statistical laws. Although there are a lot of studies on statistical laws in bulk quantum turbulence, studies in inhomogeneous or localized turbulence is scarce. We first investigate the statistical laws of localized quantum turbulence, referring to two statistical laws deduced from the vibrating wire experiments in [Yano $et$ $al.$, J. Low Temp. Phys. $196$, $184(2019)$]. The first law is the Poisson process for the detection of vortex rings; the vortex tangle emits vortex rings with frequencies depending on their sizes. The second law is the power law between the frequency and the size of the emitted vortex rings, showing the self-similarity of the tangle. To study these statistical laws numerically, we developed a system similar to experiments. First, we generate a localized statistically steady vortex tangle by injecting vortex rings from two opposite sides and causing collisions. We investigated the conditions that aid the formation of the tangles and the anisotropy of the emission of vortex rings from the tangle. Second, from the data on emitted rings, we reconstruct the two statistical laws. Results from our numerical investigations are consistent with the known self-similarity of emitted vortex rings and localized tangles.

References in corpus (18)

• Introduction to quantum turbulence
• Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation
• Sound emission due to superfluid vortex reconnections
• Energy Spectrum of Superfluid Turbulence without Normal Fluid
• Quantum hydrodynamics
• Dissipation of Quantum Turbulence in the Zero Temperature Limit
• Quantum and quasiclassical types of superfluid turbulence
• Steady State of Counterflow Quantum Turbulence: Vortex filament Simulation with the Full Biot-Savart Law
• Emergence and decay of turbulence in stirred atomic Bose-Einstein condensates
• Kolmogorov Spectrum of Quantum Turbulence
• Numerical Studies of Quantum Turbulence
• The Generation of Turbulence by Oscillating Structures in Superfluid Helium at Very Low Temperatures
• Turbulence in Boundary Flow of Superfluid ${}^4$He Triggered by Free Vortex Rings
• Fully Coupled Two-Fluid Dynamics in Superfluid ${}^4$He: Anomalous Anisotropic Velocity Fluctuations in Counterflow
• Three-Dimensional Coupled Dynamics of Two-Fluid Model in Superfluid ${}^4$He: Deformed Velocity Profile of Normal Fluid in Thermal Counterflow
• The Generation, Evolution and Decay of Pure Quantum Turbulence: A Full Biot-Savart Simulation
• Self-Organization of Vortex Length Distribution in Quantum Turbulence: An Approach from the Barabasi-Albert Model
• Statistics of vortex loops emitted from quantum turbulence driven by an oscillating sphere

Cited by in corpus (3)

• Nanoscale Real-Time Detection of Quantum Vortices at Millikelvin Temperatures
• Internal structure of localized quantized vortex tangles
• Dynamics of pinned quantized vortices in superfluid ${}^4$He in a microelectromechanical oscillator