Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$

Abstract

We discuss the energy and vorticity spectra of turbulent superfluid ${}^4$He in all the temperature range from $T=0$ up to the phase transition "$\lambda$ point", $T_{\lambda }\simeq 2.17$K. Contrary to classical developed turbulence in which there are only two typical scales, i.e. the energy injection $L$ and the dissipation scales $\eta$, here the quantization of vorticity introduces two additional scales, i.e the vortex core radius $a_0$ and the mean vortex spacing $\ell$. We present these spectra for the super- and normal-fluid components in the entire range of scales from $L$ to $a_0$ including the cross-over scale $\ell$ where the hydrodynamic eddy-cascade is replaced by the cascade of Kelvin waves on individual vortices. At this scale a bottleneck accumulation of the energy was found earlier at $T=0$. We show that even very small mutual friction dramatically suppresses the bottleneck effect due to the dissipation of the Kelvin waves. Using our results for the spectra we estimate the Vinen "effective viscosity" ${\nu }^{\prime }$ in the entire temperature range and show agreement with numerous experimental observation for ${\nu }^{\prime }(T)$.

arXiv comment20 pages, 5 figures

References in corpus (49)

• An optimal shell model of turbulence
• Transition to superfluid turbulence governed by an intrinsic parameter
• Kelvin Wave Cascade and Decay of Superfluid Turbulence
• Energy Spectrum of Superfluid Turbulence without Normal Fluid
• Dissipation of Quantum Turbulence in the Zero Temperature Limit
• Bottleneck crossover between classical and quantum superfluid turbulence
• Quantum and quasiclassical types of superfluid turbulence
• A Kelvin-wave cascade on a vortex in superfluid ${}^4$He at a very low temperature
• Spectrum of Kelvin-wave turbulence in superfluids
• Vortex density spectrum of quantum turbulence
• Quantum Turbulence
• 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
• Anomalous Scaling in a Model of Passive Scalar Advection: Exact Results
• Spectrum of turbulent Kelvin-waves cascade in superfluid helium
• Energy Spectra of Developed Turbulencein Helium Superfluids
• Quantum turbulence in propagating superfluid vortex front
• Energy cascade and the four-fifths law in superfluid turbulence
• Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling
• Towards a Nonperturbative Theory of Hydrodynamic Turbulence:Fusion Rules, Exact Bridge Relations and Anomalous Viscous Scaling Functions
• Structure of quantum vortex tangle in He-4 counterflow turbulence
• Twisted vortex state
• Energy spectra of developed superfluid turbulence
• Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
• Kelvin-wave turbulence in superfluids
• A Note on the Regularity of Inviscid Shell Model of Turbulence
• Exact Resummations in the Theory of Hydrodynamic Turbulence: II A Ladder to Anomalous Scaling
• Outliers, Extreme Events and Multiscaling
• Vortex spectrum in superfluid turbulence: interpretation of a recent experiment
• Gradual eddy-wave crossover in superfluid turbulence
• Enhancement of intermittency in superfluid turbulence
• Mesoscale Equipartition of kinetic energy in Quantum 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
• Fully developed turbulence and the multifractal conjecture
• Structure of surface vortex sheet between two rotating 3He superfluids
• Inverse Cascade Regime in Shell Models of 2-Dimensional Turbulence
• Shell model of superfluid turbulence
• Symmetries and Interaction coefficients of Kelvin waves
• Kelvin waves and the decay of quantum superfluid turbulence
• Geometric Symmetries in Superfluid Vortex Dynamics
• Cascades and dissipation ratio in rotating MHD turbulence at low magnetic Prandtl number
• Energy Spectra of Superfluid Turbulence in ${}^3$He
• On role of symmetries in Kelvin wave turbulence
• Strong Universality in Forced and Decaying Turbulence
• Temperature suppression of Kelvin-wave turbulence in superfluids
• Universal scaling exponents in shell models of turbulence: Viscous effects are finite-size corrections to scaling
• Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T = 0 superfluid turbulence" [arXiv:1201.3188]
• A stochastic model of cascades in 2D turbulence

Cited by in corpus (29)

• Cascades and transitions in turbulent flows
• Vortex clustering, polarisation and circulation intermittency in classical and quantum turbulence
• Dissipation of Quasiclassical Turbulence in Superfluid ${}^4$He
• Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence
• Dissipation in quantum turbulence in superfluid ${}^4$He above 1K
• Rotating quantum wave turbulence
• Spatio-temporal detection of Kelvin waves in quantum turbulence simulations
• Quantitative estimation of effective viscosity in quantum turbulence
• Coexistence and interplay of quantum and classical turbulence in superfluid He-4: Decay, velocity decoupling and counterflow energy spectra
• Turbulent statistics and intermittency enhancement in coflowing superfluid ${}^4$He
• ${}^4$He Counterflow Differs Strongly from Classical Flows: Anisotropy on Small Scales
• Statistics of turbulence and intermittency enhancement in superfluid ${}^4$He counterflow
• Counter-flow Induced Decoupling in Super-Fluid Turbulence
• Inhomogeneous distribution of particles in co-flow and counterflow quantum turbulence
• Counterflow-Induced Inverse Energy Cascade in Three-Dimensional Superfluid Turbulence
• Local and non-local energy spectra of superfluid ${}^3$He turbulence
• Amplitude of waves in the Kelvin-wave cascade
• Theory of energy spectra in superfluid He-4 counterflow turbulence
• Strong anisotropy of superfluid ${}^4$He counterflow turbulence
• Numerical Study on Entrance Length in Thermal Counterflow of Superfluid ${}^4$He
• Mechanical momentum transfer in wall-bounded superfluid turbulence
• Finite temperature effects in helical quantum turbulence
• Local measurement of vortex statistics in quantum turbulence
• Kelvin waves in nonequilibrium universal dynamics of relativistic scalar field theories
• Higher-order statistics and intermittency of a two-fluid HVBK quantum turbulent flow
• Disentangling temperature and Reynolds number effects in quantum turbulence
• The Statistical Properties of Superfluid Turbulence in ${}^4$He from the Hall-Vinen-Bekharevich-Khalatnikov Model
• Statistics of Quantum Turbulence in Superfluid He
• Theory of anisotropic superfluid He-4 counterflow turbulence