Steady-state counterflow quantum turbulence: Simulation of vortex filaments using the full Biot-Savart law

Adachi, Hiroyuki; Fujiyama, Shoji; Tsubota, Makoto

doi:10.1103/physrevb.81.104511

Cited by 121 publications

(217 citation statements)

References 29 publications

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“…The vortex tangle reaches the statistically steady state even if the counterflow is spatially inhomogeneous. The fluctuations are much larger than those in uniform counterflow [31] or those between two parallel plates [74,75]. The period of the oscillation is about 0.7 s, and the oscillation consists of four stages (a)-(d).…”

Section: Poiseuille and Tail-flattened Normal Flow In A Ductmentioning

confidence: 96%

“…This method enables the steady state to be sustained under periodic boundary conditions. Adachi et al performed numerical simulations using the full Biot-Savart law under periodic boundary conditions and succeeded in obtaining a statistically steady state without any unphysical procedures [31]. Figure 8(A) shows a typical result of the time evolution of the vortices, whose VLD grows as shown in Fig.…”

Section: Homogeneous Thermal Counterflowmentioning

confidence: 99%

“…Thus, when Schwarz addressed a homogeneous system under periodic boundary conditions in all three directions, he had to introduce an artificial mixing procedure. Adachi et al performed the full Biot-Savart simulation and succeeded in obtaining a steady state without the mixing procedure [31]. After the effort expended along this line, the problems of a homogeneous system were settled [32,33].…”

Section: Two-fluid Model and Thermal Counterflowmentioning

confidence: 99%

“…Schwarz assessed that the nonlocal term is not important for homogeneous quantum turbulence and performed numerical simulations of quantum turbulence by neglecting the nonlocal term, which is the LIA [30]. However, the numerical study of Adachi et al showed that the nonlocal term plays an important role even for homogeneous quantum turbulence [31].…”

Section: Motion Of Vortex Filament At 0 Kmentioning

confidence: 99%

“…This subsection reviews simulations of homogeneous counterflow of the LIA by Schwarz [30] and of the full Biot-Savart model by Adachi et al [31].…”

Section: Homogeneous Thermal Counterflowmentioning

confidence: 99%

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Numerical Studies of Quantum Turbulence

2017

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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.

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Section: Poiseuille and Tail-flattened Normal Flow In A Ductmentioning

confidence: 96%

Section: Homogeneous Thermal Counterflowmentioning

confidence: 99%

Section: Two-fluid Model and Thermal Counterflowmentioning

confidence: 99%

Section: Motion Of Vortex Filament At 0 Kmentioning

confidence: 99%

“…This subsection reviews simulations of homogeneous counterflow of the LIA by Schwarz [30] and of the full Biot-Savart model by Adachi et al [31].…”

Section: Homogeneous Thermal Counterflowmentioning

confidence: 99%

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Numerical Studies of Quantum Turbulence

2017

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Quantized Vortices and Quantum Turbulence

Tsubota

Kasamatsu

2013

Physics of Quantum Fluids

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Abstract. We review recent important topics in quantized vortices and quantum turbulence in atomic Bose-Einstein condensates (BECs). They have previously been studied for a long time in superfluid helium. Quantum turbulence is currently one of the most important topics in low-temperature physics. Atomic BECs have two distinct advantages over liquid helium for investigating such topics: quantized vortices can be directly visualized and the interaction parameters can be controlled by the Feshbach resonance. A general introduction is followed by a description of the dynamics of quantized vortices, hydrodynamic instability, and quantum turbulence in atomic BECs. IntroductionBose-Einstein condensation is often considered to be a macroscopic quantum phenomenon because bosons occupy the same single-particle ground state below the critical temperature for Bose-Einstein condensation so that they have a macroscopic wave function (order parameter) Ψ (r, t) = |Ψ (r, t)|e iθ(r,t) that extends over the entire system. Here, the absolute squared amplitude |Ψ | 2 = n gives the condensate density and the gradient of the phase θ(r, t) gives the superfluid velocity field v s = (h/m)∇θ with boson mass m as the potential flow. Since the macroscopic wave function should be single-valued for the space coordinate r, the circulation Γ = v s · dℓ for an arbitrary closed loop in the fluid will be quantized with the quantum κ = h/m. A vortex with such quantized circulation is known as a quantized vortex. Any rotational motion of a superfluid is sustained only by quantized vortices. Hydrodynamics dominated by quantized vortices is called quantum hydrodynamics (QHD), and turbulence comprised of quantized vortices is known as quantum turbulence (QT).A quantized vortex is a stable topological defect that is a characteristic of a Bose-Einstein condensate (BEC). It differs from a vortex in a classical

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Waves on a vortex filament: exact solutions of dynamical equations

Brugarino

Mongiovı̀

Sciacca

2014

Z. Angew. Math. Phys.

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In this paper, we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded, and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.

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Steady-state counterflow quantum turbulence: Simulation of vortex filaments using the full Biot-Savart law

Cited by 121 publications

References 29 publications

Numerical Studies of Quantum Turbulence

Numerical Studies of Quantum Turbulence

Quantized Vortices and Quantum Turbulence

Waves on a vortex filament: exact solutions of dynamical equations

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