Classical character of turbulence in a quantum liquid

We capture the decay of a quantized vortex ring in superfluid helium-4 by imaging particles trapped on the vortex core. The ring shrinks in time, providing direct evidence for the dissipation of energy in the superfluid. The ring with trapped particles collapses more slowly than predicted by an available theory, but the collapse rate can be predicted correctly if the trapping of the particles on the core is taken into account. We theoretically explore the conditions under which particles may be considered passive tracers of quantized vortices and estimate, in particular, that their dynamics on the large-scale is largely unaffected by the burden of trapped particles if the latter are spaced by more than ten particle diameters along the vortex core, at temperatures between 1.5 K and 2.1 K.

Section: The Governing Equationmentioning

confidence: 99%

The Decay of a Quantized Vortex Ring and the Influence of Tracer Particles

Bewley

Sreenivasan

2009

“…The latter issue was tackled by Morris et al [34] who employed fully developed Navier-Stokes turbulence in order to generate superfluid turbulence, and found a tendency of alignment between the large scale averages of the two vorticities. There was, however, no explicit information on the formation of superfluid bundles and their trapping by coherent normal vortical structures or their combined subsequent movement as one fully coupled vortical structure as suggested by Vinen [27]. Notwithstanding the sophistication of their computation, Morris et al did not offer an explicit mechanism for the alignment process, and did not employ the local normal flow velocity formulation of the mutual friction forces that is consistent with their fully resolved Navier-Stokes turbulence in the normal fluid.…”

mentioning

confidence: 99%

“…Previously, Vinen [27] modeled turbulence eddies in both fluids as rigid spheres, and by employing dimensional and scaling analysis, as well as an approximate formula for the mutual friction force, concluded that under certain conditions the large scale dynamics of the two fluids would be identical (fully coupled). This understanding, which is also employed in the analysis of Stalp et al [15] indicates a much stronger effect than a simple tendency of alignment between the vorticity of the two fluids.…”

mentioning

confidence: 99%

Elementary Vortex Processes in Thermal Superfluid Turbulence

Kivotides

Wilkin

2009

By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics.

“…Although our understanding of superfluid turbulence and vortex dynamics has made significant gains, the relation between superfluid turbulence and classical turbulence remains a major unsolved problem [23,24]. Probably, this situation has arisen because most studies of superfluid turbulence have been devoted to thermal counterflow which has no analogy with classical turbulence.…”

Section: B Recent Studies On Superfluid Turbulencementioning

confidence: 99%

“…This means the presence of the definite inertial range in which the energy is transferred from large scale to smaller scales by the Richardson cascade process. The resulting small vortices whose size becomes close to the coherence length would be unable to keep its vortex nature to change into some elementary excitations, or dissipate by acoustic emission [24], but the inertial range should be independent of such dissipative mechanisms. Second, superfluid turbulence is made of a tangle of quantized vortices.…”

Section: B Recent Studies On Superfluid Turbulencementioning

confidence: 99%

Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates

Tsubota

Kasamatsu

2005

In this article, we review the research on the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates with emphasis on the recent research done by our group. A quantized vortex is a topological defect that arises from the order parameter in Bose-Einstein condensation in which frictionless superfluid flows with quantized circulation around each vortex.A quantized vortex was both predicted and discovered first in superfluid 4 He which was the first example of a Bose-Einstein condensate. Quantized vortices have been thoroughly studied in superfluid 4 He; one of the principal problems was the superfluid turbulent state consisting of a tangle of quantized vortices in thermal counterflow. More recently, the interest has shifted to the nature of superfluid turbulence, apart from the case of counterflow. After briefly reviewing the earlier research and describing the current problems, we focus our review on superfluid turbulence and vortex filament dynamics. One of the important problems is how superfluid turbulence relates to classical turbulence. Superfluid turbulence was recently shown to have an energy spectrum consistent with the Kolmogorov law, which is an important statistical law in fully developed classical turbulence. We also describe the diffusion of an inhomogeneous vortex tangle with relation to the observed decay of vortices at very low temperatures where the normal fluid component is so negligible that the usual mutual friction does not work as a decay mechanism. In connection to the above discussion of groups of vortices, we describe the vortex states that appear in a rotating channel with counterflow. Rotational effects cause the vortices to form ordered arrays, whereas counterflow effects tend to cause disordered vortex tangles; the competition of these two effects makes a new state of "a polarized vortex tangle" which opens up superfluid phase diagrams as a new area of study.In the specific field of atomic-gas Bose-Einstein condensation, we discuss recent numerical analysis of the Gross-Pitaevskii equation that describes the structure and dynamics of the order parameter. Consistent with observations, the simulated condensate starts an elliptic oscillation after the rotation is turned on, which induces the surface-mode excitations. The vortices develop from these surface excitations and then enter the bulk condensate, eventually forming a vortex lattice. When a condensate is held in a quadratic-plus-quartic combined potential, the fast rotation makes "a giant vortex" in which most vortices are absorbed into a central hole around which the superflow circulates.