Quantitative estimation of effective viscosity in quantum turbulence

Abstract

We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$ grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale $\ell$, and a second inertial range for scales smaller than $\ell$. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite temperature effects in the decay of quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions using the GPE. We extract the mean free path out of these simulations by measuring the spectral broadening in the Bogoliubov dispersion relation obtained from spatio-temporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, in order to compare the decay of high temperature quantum and that of classical flows, and to further calibrate the estimations of viscosity from the mean free path in the GPE simulations, we perform low Reynolds number simulations of the Navier-Stokes equations.

arXiv comment15 figures, Supplemental material: Video M1 and M2

References in corpus (29)

• Emergence of turbulence in an oscillating Bose-Einstein condensate
• Introduction to quantum turbulence
• Finite Temperature Models of Bose-Einstein Condensation
• Simulations of Bose fields at finite temperature
• Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation
• Bottleneck crossover between classical and quantum superfluid turbulence
• Quantum turbulence in trapped atomic Bose-Einstein condensates
• Vortices and turbulence in trapped atomic condensates
• Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate
• Spectrum of Kelvin-wave turbulence in superfluids
• Energy cascade with small-scales thermalization, counterflow metastability and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation
• Quantification of the strength of inertial waves in a rotating turbulent flow
• Quantum turbulence at finite temperature: the two-fluids cascade
• Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
• Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation
• Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates
• Dual cascade and dissipation mechanisms in helical quantum turbulence
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• Enhancement of intermittency in superfluid turbulence
• Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence
• Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation
• Spatio-temporal detection of Kelvin waves in quantum turbulence simulations
• Shell model of superfluid turbulence
• Turbulent statistics and intermittency enhancement in coflowing superfluid ${}^4$He
• Multiscaling in superfluid turbulence: A shell-model study
• Homogeneous Isotropic Superfluid Turbulence in Two Dimensions: Inverse and Forward Cascades in the Hall-Vinen-Bekharevich-Khalatnikov model
• Visualization of quantum turbulence in superfluid ${}^3$He-B: Combined numerical/experimental study of Andreev reflection
• Stochastic Gross-Pitaevsky Equation for BEC via Coarse-Grained Effective Action
• Finite temperature effects in helical quantum turbulence

Cited by in corpus (19)

• Decaying quantum turbulence in a two-dimensional Bose-Einstein condensate at finite temperature
• Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence
• Abrupt transition between three and two-dimensional quantum turbulence
• Self-similar evolution of wave turbulence in Gross-Pitaevskii system
• Quantum engines with interacting Bose-Einstein condensates
• Kolmogorov and Kelvin wave cascades in a generalized model for quantum turbulence
• Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory
• Thermalized Abrikosov lattices from decaying turbulence in rotating BECs
• Fermionic Quantum Turbulence: Pushing the Limits of High-Performance Computing
• Active and finite-size particles in decaying quantum turbulence at low temperature
• Stochastic motion of finite-size immiscible impurities in a dilute quantum fluid at finite temperature
• Dimensional measures of generalized entropy
• Comment on "Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory''
• Toy Model for Vortex Ring-Assisted Particle Drag in Superfluid Counterflow
• Finite-time thermal refrigerator in interacting Bose-Einstein Condensates
• Vortices in a Ginzburg Landau Theory of Superconductors with Nematic Order
• Turbulence in rotating Bose-Einstein condensates
• Reply to "Comment on 'Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory'"
• Conformal invariance in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii Equation