Kelvin waves and the decay of quantum superfluid turbulence

Abstract

We present a comprehensive statistical study of free decay of the quantized vortex tangle in superfluid ${}^4$He at low and ultra-low temperatures, $0⩽T⩽1.1$K. Using high resolution vortex filament simulations with full Biot-Savart vortex dynamics, we show that for ultra-low temperatures $T\lesssim 0.5$K, when the mutual friction parameters $\alpha \simeq {\alpha }^{\prime }<10^{-5}$, the vortex reconnections excite Kelvin waves with wave lengths $\lambda$ of the order of the inter-vortex distance $\ell$. These excitations cascade down to the resolution scale $\Delta \xi$ which in our simulations is of the order $\Delta \xi \sim \ell /100$. At this scale the Kelvin waves are numerically damped by a line-smoothing procedure, that is supposed to mimic the dissipation of Kelvin waves by phonon and roton emission at the scale of the vortex core. We show that the Kelvin waves cascade is statistically important: the shortest available Kelvin waves at the end of the cascade determine the mean vortex line curvature $S$, giving $S\gtrsim 30/\ell$ and play major role in the tangle decay at ultra-low temperatures below $0.6$K. The found dependence of $\ell S$ on the resolution scale $\Delta \xi$ agrees with the L'vov-Nazarenko energy spectrum of weakly-interacting Kelvin waves, $E\Sb{LN}\propto k^{-5/3}$ rather than the spectrum $E\Sb{LN}\propto k^{-1}$, suggested by Vinen for turbulence of Kelvin waves with large amplitudes. We also show that already at $T=0.8$K, when $\alpha$ and ${\alpha }^{\prime }$ are still very low, $\alpha \simeq {\alpha }^{\prime }<10^{-3}$, the Kelvin wave cascade is fully damped, vortex lines are very smooth, $S\simeq 2/\ell$ and the tangle decay is predominantly caused by the mutual friction.

arXiv comment11 pages, 7 figs, PRB in press, Sept. 2014

References in corpus (31)

• Introduction to quantum turbulence
• Kelvin Wave Cascade and Decay of Superfluid Turbulence
• Energy Spectrum of Superfluid Turbulence without Normal Fluid
• Quantum and quasiclassical types of superfluid turbulence
• Dynamics of vortex tangle without mutual friction in superfluid ${}^4$He
• A Kelvin-wave cascade on a vortex in superfluid ${}^4$He at a very low temperature
• Steady State of Counterflow Quantum Turbulence: Vortex filament Simulation with the Full Biot-Savart Law
• Spectrum of Kelvin-wave turbulence in superfluids
• The interaction of Kelvin waves and the non-locality of the energy transfer in superfluids
• Vortex filament method as a tool for computational visualization of quantum turbulence
• Spectrum of turbulent Kelvin-waves cascade in superfluid helium
• Quantum turbulence in propagating superfluid vortex front
• Turbulent dynamics in rotating helium superfluids
• Scale Separation Scheme for Simulating Superfluid Turbulence: Kelvin-Wave Cascade
• Structure of quantum vortex tangle in He-4 counterflow turbulence
• Cascade of vortex loops initiated by a single reconnection of quantum vortices
• Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
• Quantum turbulence at finite temperature: the two-fluids cascade
• Kelvin-wave turbulence in superfluids
• Vortex--Phonon Interaction
• Differential approximation for Kelvin-wave turbulence
• The Kelvin-wave cascade in the vortex filament model
• Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence
• Dissipation enhancement from a single vortex reconnection in superfluid helium
• Symmetries and Interaction coefficients of Kelvin waves
• Geometric Symmetries in Superfluid Vortex Dynamics
• On role of symmetries in Kelvin wave turbulence
• Temperature suppression of Kelvin-wave turbulence in superfluids
• Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T = 0 superfluid turbulence" [arXiv:1201.3188]
• Decay of Counterflow Quantum Turbulence in Superfluid ^4He
• Reply to Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence" [arXiv:1208.4593]

Cited by in corpus (12)

• Quantum turbulence in trapped atomic Bose-Einstein condensates
• Quantum turbulence in quantum gases
• Dissipation of Quasiclassical Turbulence in Superfluid ${}^4$He
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• Rotating quantum turbulence in the unitary Fermi gas
• Spatio-temporal detection of Kelvin waves in quantum turbulence simulations
• Coexistence of quantum and classical flows in quantum turbulence in the $T=0$ limit
• Nanomechanical resonators for cryogenic research
• Counter-flow Induced Decoupling in Super-Fluid Turbulence
• Interactions between unidirectional quantized vortex rings
• Kelvin waves from vortex reconnection in superfluid helium at low temperatures
• Radial vortex core oscillations in Bose-Einstein condensates