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 0.5 K, when the mutual friction parameters α ≃ α ′ < 10 −5 , the vortex reconnections excite Kelvin waves with wave lengths λ of the order of the inter-vortex distance ℓ. These excitations cascade down to the resolution scale ∆ξ which in our simulations is of the order ∆ξ ∼ ℓ/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 30/ℓ and play major role in the tangle decay at ultra-low temperatures below 0.6 K. The found dependence of ℓS on the resolution scale ∆ξ agrees with the L'vov-Nazarenko energy spectrum of weakly-interacting Kelvin waves, ELN ∝ k −5/3 rather than the spectrum ELN ∝ k −1 , suggested by Vinen for turbulence of Kelvin waves with large amplitudes. We also show that already at T = 0.8 K, when α and α ′ are still very low, α ≃ α ′ < 10 −3 , the Kelvin wave cascade is fully damped, vortex lines are very smooth, S ≃ 2/ℓ and the tangle decay is predominantly caused by the mutual friction.

Coexistence of Quantum and Classical Flows in Quantum Turbulence in TheT=0Limit

“…with t V = γ ζκL0 (where L 0 = L(0)). Such decay with a universal prefactor, corresponding to ζ ≈ 0.10, was observed in QT generated after a brief injection of ions in cells of different sizes [11,13] and also in numerical simulations of Vinen QT [25,26].…”

Quantum turbulence in trapped atomic Bose–Einstein condensates

“…In superfluids it has been suggested that cascades of Kelvin waves can transfer energy from the scale of the intervortex spacing down to smaller scales, as small as the vortex core [106,55,144]. Therefore, Kelvin modes become an important mechanism in the decay of turbulence [94] as energy is directed to the smaller scales of the system, where it is eventually dissipated.…”

Dissipation enhancement from a single vortex reconnection in superfluid helium

“…21 Our method of making a reconnection follows that of other authors. 17,[22][23][24][25] Traditionally one reconnects two vortices as soon as any two points approach closer than some given distance. This critical distance is typically taken to be of the order of the resolution.…”