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

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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
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• 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
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• The system of the vortex-like structures: the viewpoint on a turbulence modelling
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• Driven-dissipative turbulence in exciton-polariton quantum fluids
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• 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