Numerical Studies of Quantum Turbulence

Abstract

We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose--Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross--Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed in revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose--Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates e.g. two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, $etc.$, some of which has not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally we discuss open problems.

76 pages, 32 figures

References in corpus (95)

• Vortex formation in a stirred Bose-Einstein condensate
• Spinor Bose Condensates in Optical Traps
• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• Bose-Einstein condensation with internal degrees of freedom in alkali atom gases
• Spinor Bose-Einstein condensates
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Observation of vortex dipoles in an oblate Bose-Einstein condensate
• Driving phase slips in a superfluid atom circuit with a rotating weak link
• Emergence of turbulence in an oscillating Bose-Einstein condensate
• Introduction to quantum turbulence
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Observation of vortex phase singularities in Bose-Einstein condensates
• Directed percolation criticality in turbulent liquid crystals
• Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate
• Spontaneously modulated spin textures in a dipolar spinor Bose-Einstein condensate
• Quantised supercurrent decay in an annular Bose-Einstein condensate
• Emergence of a Turbulent Cascade in a Quantum Gas
• Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation
• Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid
• A Universal Transition to Turbulence in Channel Flow
• Kelvin Wave Cascade and Decay of Superfluid Turbulence
• Quantum hydrodynamics
• Energy Spectrum of Superfluid Turbulence without Normal Fluid
• Dissipation of Quantum Turbulence in the Zero Temperature Limit
• Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates
• Quantum and quasiclassical types of superfluid turbulence
• Inverse Energy Cascade in Forced 2D Quantum Turbulence
• Quantum Turbulence in a Trapped Bose-Einstein Condensate
• Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas
• Emergence of order from turbulence in an isolated planar superfluid
• 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
• Wave turbulence and vortices in Bose-Einstein condensation
• Visualization study of counterflow in superfluid helium-4 using metastable helium molecules
• Superfluid Turbulence: Nonthermal Fixed Point in an Ultracold Bose Gas
• Onsager-Kraichnan Condensation in Decaying Two-Dimensional Quantum Turbulence
• Binary Quantum Turbulence Arising from Countersuperflow Instability in Two-Component Bose-Einstein Condensates
• Visualization of the normal-fluid turbulence in counterflowing superfluid 4He
• Critical Dynamics of a Two-dimensional Superfluid near a Non-Thermal Fixed Point
• Turbulent velocity spectra in superfluid flows
• Direct Energy Cascade in Two-Dimensional Compressible Quantum Turbulence
• Finite temperature vortex dynamics in Bose Einstein condensates
• Kolmogorov Spectrum of Quantum Turbulence
• Classical and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates
• The Generation of Turbulence by Oscillating Structures in Superfluid Helium at Very Low Temperatures
• Visualization of Superfluid Helium Flow
• Decay of a quantum vortex: test of non-equilibrium theories for warm Bose-Einstein condensates
• The interaction of Kelvin waves and the non-locality of the energy transfer in superfluids
• Energy cascades and spectra in turbulent Bose-Einstein condensates
• Creation and characterization of vortex clusters in atomic Bose-Einstein condensates
• Spectral energy transport in two-dimensional quantum vortex dynamics
• Generation and Decay of Two-Dimensional Quantum Turbulence in a Trapped Bose-Einstein Condensate
• Energy cascade and the four-fifths law in superfluid turbulence
• Coherent vortex structures in quantum turbulence
• Onsager vortex formation in Bose-Einstein condensates in two-dimensional power-law traps
• A geometrical approach to the dynamics of spinor condensates II: Collective modes
• A geometrical approach to the dynamics of spinor condensates I: Hydrodynamics
• Reconnection of superfluid vortex bundles
• Countersuperflow instability in miscible two-component Bose-Einstein condensates
• Metastable helium molecules as tracers in superfluid liquid ${}^4$He
• Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling
• Structure of quantum vortex tangle in He-4 counterflow turbulence
• Long wavelength spin dynamics of ferromagnetic condensates
• Hydrodynamic Description of Spin-1 Bose-Einstein Condensates
• Universal scaling at non-thermal fixed points of a two-component Bose gas
• A superfluid boundary layer
• Collisional Dynamics of Half-Quantum Vortices in a Spinor Bose-Einstein Condensate
• Counterflow instability and turbulence in a spin-1 spinor Bose--Einstein condensate
• The sensitivity of the vortex filament method to different reconnection models
• Vortex line density in counterflowing He II with laminar and turbulent normal fluid velocity profiles
• Polarization of superfluid turbulence
• Dynamics of quantum turbulence of different spectra
• Magnetic Richtmyer-Meshkov instability in a two-component Bose-Einstein condensate
• Tuning universality far from equilibrium
• Tree method for quantum vortex dynamics
• Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid
• Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence
• The Kelvin-wave cascade in the vortex filament model
• Hydrodynamic equation of a spinor dipolar Bose-Einstein condensate
• Counterflow quantum turbulence of He II in a square channel: Numerical analysis with nonuniform flows of the normal fluid
• Turbulence in Binary Bose-Einstein Condensates Generated by Highly Non-Linear Rayleigh-Taylor and Kelvin-Helmholtz Instabilities
• Thermal counterflow in a periodic channel with solid boundaries
• Bogoliubov-wave turbulence in Bose-Einstein condensates
• Coupled normal fluid and superfluid profiles of turbulent helium II in channels
• Coexistence and interplay of quantum and classical turbulence in superfluid He-4: Decay, velocity decoupling and counterflow energy spectra
• A route to non-Abelian quantum turbulence in spinor Bose-Einstein condensates
• Velocity-dependent quantum phase slips in 1D atomic superfluids
• Dissipative hydrodynamic equation of a ferromagnetic Bose-Einstein condensate: Analogy to magnetization dynamics in conducting ferromagnets
• Quantum turbulence by vortex stirring in a spinor Bose-Einstein condensate
• Vortex dynamics in rotating counterflow and plane Couette and Poiseuille turbulence in superfluid Helium
• Coupled dynamics for superfluid ${}^4$He in the channel
• Logarithmic velocity profile of quantum turbulence of superfluid ${}^4$He
• Counterflow quantum turbulence in a square channel under the normal fluid with a Poiseuille flow
• Expansion of a Bose-Einstein Condensate with Vortices

Cited by in corpus (51)

• Order from chaos: Observation of large-scale flow from turbulence in a two-dimensional superfluid
• Vortices in self-bound dipolar droplets
• Quantum turbulence in quantum gases
• Vortex properties in the extended supersolid phase of dipolar Bose-Einstein condensates
• Universal dynamics of a turbulent superfluid Bose gas
• Dissipative shock waves generated by a quantum-mechanical piston
• Intermittency of velocity circulation in quantum turbulence
• 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
• Coherent and incoherent structures in fuzzy dark matter halos
• Edge wave and boundary layer of vortex matter
• Emergent Non-Eulerian Hydrodynamics of Quantum Vortices in Two Dimensions
• Universal equation of state for wave turbulence in a quantum gas
• 2D Quantum Turbulence in Polariton Condensates
• Vorticity and quantum turbulence in the merging of superfluid Helium nanodroplets
• Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics
• Motion of a superfluid vortex according to holographic quantum dissipation
• Quantum turbulence simulations using the Gross-Pitaevskii equation: high-performance computing and new numerical benchmarks
• Dissipative Dynamics of Quantum Vortices in Fermionic Superfluid
• Phase separation of quantized vortices in two-component miscible Bose-Einstein condensates in a two-dimensional box potential
• Visualisation of quantised vortex reconnection as enabled by laser ablation
• Magnon Bose-Einstein condensates: from time crystals and quantum chromodynamics to vortex sensing and cosmology
• Anti-glitches in accreting pulsars from superfluid vortex avalanches
• Fermionic Quantum Turbulence: Pushing the Limits of High-Performance Computing
• Small Oscillations of a Vortex Ring: Hamiltonian Formalism and Quantization
• Statistical laws and self-similarity of vortex rings emitted from a localized vortex tangle in superfluid ${}^4$He
• Direct excitation of Kelvin waves on quantized vortices
• Particle approximation of the two-fluid model for superfluid ${}^4$He using smoothed particle hydrodynamics
• Entropy of a Turbulent Bose-Einstein Condensate
• Closed Vortex Filament in a Cylindrical Domain: Circulation Quantization
• The turbulence development at its initial stage: a scenario based on the idea of vortices decay
• Towards quantum turbulence theory: A simple model with interaction of the vortex loops
• Topological turbulence in spin-orbit-coupled driven-dissipative quantum fluids of light generates high angular momentum states
• Internal structure of localized quantized vortex tangles
• Dynamics of two quantized vortices belonging to different components of binary Bose-Einstein condensates in a circular box potential
• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
• The system of the vortex-like structures: the viewpoint on a turbulence modelling
• Higher-order statistics and intermittency of a two-fluid HVBK quantum turbulent flow
• Dynamics of pinned quantized vortices in superfluid ${}^4$He in a microelectromechanical oscillator
• Driven-dissipative turbulence in exciton-polariton quantum fluids
• Dissipation and Decay of Three Dimensional Holographic Quantum Turbulence
• Annihilation and recurrence of vortex-antivortex pairs in two-component Bose-Einstein condensates
• Rayleigh-Taylor, Kelvin-Helmholtz and immiscible to miscible quenching instabilities in binary Bose-Einstein condensates
• Excitation spectrum of vortex-lattice modes in a rotating condensate with a density-dependent gauge potential
• Vortex Simulations on a 3-Sphere
• Toy Model for Vortex Ring-Assisted Particle Drag in Superfluid Counterflow
• An Equation of State for Turbulence in the Gross-Pitaevskii model
• Merging of superfluid Helium nanodroplets with vortices
• Studies on quantum turbulence with Vinen
• Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows
• Conformal invariance in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii Equation