Numerical analysis of quantum turbulence created by oscillating objects : Universal law underlying classical and quantum turbulence

Audun Skaugen, Luiza Angheluta

Matthew T. Reeves

Turbulence, the irregular motion of fluids, is a challenging problem in physics. Yet some properties of turbulence appear to be universal, independent of the underlying host fluid supporting the motion. Recent studies have found that turbulence in superfluid helium, a quantum fluid, exhibits two of the most fundamental laws of classical fluid turbulence: the Kolmogorov −5/3 law, and the dissipation anomaly. These laws appear despite the fluid being highly constrained by quantum mechanical effects, and completely lacking kinematic viscosity. Such findings suggest further insight into the universal features of turbulent phenomena can be gained by studying analogies between classical and quantum turbulence.\nAtomic Bose-Einstein condensates (BECs) offer a new platform for the study of quantum turbulence; the geometric control available in BEC experiments offers the possibility of studying quantum turbulence in effectively two-dimensional fluids. As two-dimensional turbulence exhibits dramatically different features from its 3D counterpart, BEC systems allow for further study of the analogies between classical and quantum turbulence. In this thesis we numerically and theoretically study 2D quantum turbulence in BECs within the framework of the Gross-Pitaevskii model. We focus on analogies with classical 2D turbulence, with the aim of identifying common or universal features.\nFirst we investigate coherent vortex structures in negative temperature equilibria via an experimentally accessible flow-field measure. Coherent vortices are shown to produce a clear signal in this measure that is independent of the confinement geometry, and we demonstrate that it can be observed in dynamical simulations.\nSecond, studying a quantum analogue of the two-dimensional cylinder wake, we investigate the phenomenon of Strouhal oscillations. We find that the Strouhal number obeys a universal relation, similar to the classical form, upon introducing a modified superfluid Reynolds number that accounts for the critical velocity for vortex nucleation. Like the classical Reynolds number, the superfluid Reynolds number is found to govern the transition from laminar to turbulent behaviour in the quantum fluid.\nFinally, simulating decaying 2D quantum turbulence for very large vortex numbers, we show that quantum fluids are capable of supporting the direct enstrophy cascade, a fundamental feature of two-dimensional turbulent flows. The quantum fluid manifests key features of the classical cascade, including Batchelor’s −3 law of the inertial range, scaling of the inertial range against the superfluid Reynolds number, and the value of the Kraichnan-Batchelor constant.\nThe findings from this work thus provide some new insight into the universality of fundamental turbulence concepts, and their applicability to quantum fluids.

Makoto Tsubota

M. T. M. Christenhusz, Arghavan Safavi-Naini, Halina H. Rubinsztein-Dunlop +2 more

Despite the fundamentally different dissipation mechanisms, many laws and phenomena of classical turbulence equivalently manifest in quantum turbulence. The Reynolds law of dynamical similarity states that two objects of the same geometry across different length scales are hydrodynamically equivalent under the same Reynolds number, leading to a universal drag coefficient law. In this Letter we confirm the existence of a universal drag law in a superfluid wake, facilitated by the nucleation of quantized vortices. We numerically study superfluid flow across a range of Reynolds numbers for the paradigmatic classical hard wall and the Gaussian obstacle, popular in experimental quantum hydrodynamics. In addition, we provide a feasible method for measuring superfluid drag forces in an experimental environment using control volumes.

Ionut Danaila, Luminita Danaila, Zhentong Zhang

Michikazu Kobayashi, Makoto Tsubota

We investigated dynamics of superfluid turbulence by the Gross-Pitaevskii equation and its relation to conventional classical turbulence. We introduced the dissipation term which is effective only in the scale smaller than the core size of quantized vortices, and found that the energy spectrum of superfluid turbulence was consistent with the Kolmogorov law which is one of the most important statistical laws of classical turbulence.