Vortex filament method as a tool for computational visualization of quantum turbulence

Abstract

The vortex filament model has become a standard and powerful tool to visualize the motion of quantized vortices in helium superfluids. In this article, we present an overview of the method and highlight its impact in aiding our understanding of quantum turbulence, particularly superfluid helium. We present an analysis of the structure and arrangement of quantized vortices. Our results are in agreement with previous studies showing that under certain conditions, vortices form coherent bundles, which allows for classical vortex stretching, giving quantum turbulence a classical nature. We also offer an explanation for the differences between the observed properties of counterflow and pure superflow turbulence in a pipe. Finally, we suggest a mechanism for the generation of coherent structures in the presence of normal fluid shear.T urbulence in fluid flows is universal, from galactic scales generated by supernova explosions down to an aggressively stirred cup of coffee. There is no debate that turbulence is important, yet no satisfactory theory exists. Turbulence is built by rotational motions, typically over a wide range of scales, interacting and mediating a transfer of energy to scales at which it can be dissipated effectively. The motivation for Küchemann's famous quote "vortices are the sinews and muscles of fluid motions" is clear. If this is true, then quantum turbulence (QT) represents the skeleton of turbulence and offers a method of attacking the turbulence problem in perhaps its simplest form.QT is a tangle of discrete, thin vortex filaments, each carrying a fixed circulation. It typically is studied in cryogenically cooled helium (1, 2) and, more recently, in atomic Bose-Einstein condensates (3). These substances are examples of so-called quantum fluids: fluids for which certain physical properties cannot be described classically but depend on quantum mechanics. The quantization of vorticity is one marked difference between quantum and classical fluids. Another is their two-fluid nature; they consist of a viscous normal fluid component and an inviscid superfluid component coupled by a mutual friction. The relative densities of these components are temperature dependent.Despite these marked differences, it is now the consensus opinion that QT is capable of exhibiting many of the statistical properties of classical turbulence, including the famed Kolmogorov scaling (4). Hence, QT has the potential to offer new insights into vortex dynamics and the role they play in the dynamics of turbulence. In addition, QT offers many interesting problems in its own right. However, QT, more so than classical turbulence, suffers from poor visualization of the flow in experiments because of the extremely low temperatures involved. Hence, numerical methods are necessary to aid our understanding of the structure of quantized vortices in different forms of turbulence, acting as a guide for both experiments and theory. In this article, we discuss a widely used numerical model of QT, the vortex filament model (VFM). VFMIn the ...

Coupled motion of Xe clusters and quantum vortices in He nanodroplets

“…The shapes and dynamics of bare vortices with fixed boundary conditions can, in principle, be calculated using the BiotSavart law [30][31][32][33]. However, the implementation of this approach is not straightforward due to the additional acquired mass of the dopant atoms and a possible vorticity-dependence of the droplet shape.…”

Crossover from interaction to driven regimes in quantum vortex reconnections

“…Reconnections of coherent filamentary structures ( Fig. 1) play a fundamental role in the dynamics of plasmas (from astrophysics [1][2][3] to confined nuclear fusion), nematic liquid crystals [4], polymers and macromolecules [5] (including DNA [6]), optical beams [7,8], ordinary (classical) fluids [9][10][11] and quantum fluids [12,13]. In fluids, the coherent structures consist of concentrated vorticity, whose character depends on the classical or quantum nature of the fluid: in classical fluids (air, water etc.…”

Vortex reconnections in atomic condensates at finite temperature

“…However, we may gain some insight to the temperature-independence of the reconnecting behaviour from it. In the BiotSavart model [43] the vortex is a three-dimensional space curve s ≡ s(ς, t) of infinitesimal thickness, where ς is arc length. The velocity of the curve at the point s is v L = v si − αs × v si , where v si is the self-induced velocity (determined by a Biot-Savart integral over the entire vortex configuration), s ≡ ds /dς is the unit tangent vector at s, and α is a dimensionless temperature dependent friction parameter.…”