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.

Fully Coupled Two-Fluid Dynamics in Superfluid He4 : Anomalous Anisotropic Velocity Fluctuations in Counterflow

“…Quantum turbulence (QT) refers to the turbulent state of the superfluid component. Lots of studies have examined QT [15][16][17][18][19][20] since Feynman's suggestion [21]. QT is a tangle of quantized vortices, and this tangle produces a turbulent velocity field of the superfluid.…”

“…Coupled dynamics of quantized vortices and normal fluid.-The VFM is used as one of the most powerful tools to describe the dynamics of quantized vortices [20,[46][47][48][49][50][51][52][53][54][55][56]. The position vector s of the filaments are represented by the parametric form s = s(ξ) with arc length ξ.…”

Three-Dimensional Coupled Dynamics of the Two-Fluid Model in Superfluid He4 : Deformed Velocity Profile of Normal Fluid in Thermal Counterflow

“…The system most characteristic of the two-fluid model is thermal counterflow in superfluid 4 He, which exhibits a typical stage of quantum hydrodynamics and quantum turbulence [8][9][10][11][12]. In usual experiments of thermal counterflow, superfluid 4 He is confined within a channel, with one closed end and the other end connected to a helium bath.…”

Quantum Turbulence in Quantum Gases

“…A survey on simulations using the GP model, and several other numerical methods applied to QT, can be found in Ref. (55).…”