Evaporation of a packet of quantized vorticity

We study the diffusion of a packet of quantized vorticity initially confined inside a small region. We find that reconnections fragment the packet into a gas of small vortex loops which fly away. The time scale of the process is in order-of-magnitude agreement with recent experiments performed in 3He-B.     

Rotating superfluid turbulence

Almost all studies of vortex states in helium II have been concerned with either ordered vortex arrays or disordered vortex tangles. This work numerically studies what happens in the presence of both rotation (which induces order) and thermal counterflow (which induces disorder). We find a new statistically steady state in which the vortex tangle is polarized along the rotational axis. Our results are used to interpret an instability that was discovered experimentally by Swanson et al. [Phys. Rev. Lett. 50, 190 (1983)]] and the vortex state beyond the instability that has been unexplained until now.     

Sound emission due to superfluid vortex reconnections

By performing numerical simulations based on the Gross-Pitaevskii equation, we make direct quantitative measurements of the sound energy released due to superfluid vortex reconnections. We show that the energy radiated expressed in terms of the loss of vortex line length is a simple function of the reconnection angle. In addition, we study the temporal and spatial distribution of the radiation and show that energy is emitted in the form of a sound pulse with a wavelength of a few healing lengths.     

A numerical investigation of vortex-coupled superfluidity

We have performed numerical simulations of quantized vortex lines in a model of normal fluid turbulence. The results are used to discuss the idea, put forward to explain some recent experiments, that in isothermal turbulent helium flow the high density of vortex lines locks the two fluid components together.     

Stretching in a model of a turbulent flow

Using a multi-scaled, chaotic flow known as the KS model of turbulence [J.C.H. Fung, J.C.R. Hunt, A. Malik, R.J. Perkins, Kinematic simulation of homogeneous turbulence by unsteady random fourier modes, J. Fluid Mech. 236 (1992) 281-318], we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov exponents are sensitive to the advection of small eddies by large eddies, which can be explained by considering the Lagrangian correlation time of the smallest scales. We also relate the number of stagnation points within a flow to the maximum Lyapunov exponent, and suggest a linear dependence between the two characteristics.     

Absolute measurement of vortex line density in counterflowing hell

The vortex line density in a thermally induced counterflow in helium II is measured by means of attenuation of second sound in a long channel 1 cm × 1 cm in cross section. The line density is calibrated by rotating the channel about its vertical axis. The results are compared with current theories of vortex line turbulence.     

Vortex nucleation by collapsing bubbles in Bose-Einstein condensates

Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be 28+/-1 healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.     

Magnetic structures produced by the small-scale dynamo

Small-scale dynamo action has been obtained for a flow previously used to model fluid turbulence, where the sensitivity of the magnetic field parameters to the kinetic energy spectrum can be explored. We apply quantitative morphology diagnostics, based on the Minkowski functionals, to magnetic fields produced by the kinematic small-scale dynamo to show that magnetic structures are predominantly filamentary rather than sheetlike. Our results suggest that the thickness, width, and length of the structures scale differently with magnetic Reynolds number as R(m)(-2/(1-s)) and R(m)(-0.55} for the former two, whereas the latter is independent of R(m), with s the slope of the energy spectrum.     

Fractal dimension of superfluid turbulence

Superfluid turbulence consists of a disordered tangle of quantized vortex filaments which interact with each other and with the normal fluid. We develop a kinematic model of normal-fluid turbulence to study superfluid vortex tangles at finite temperatures and show by numerical simulation that the system of filaments has a fractal dimension larger than one. We find that the fractal dimension is directly related to the vortex-line density and is independent of temperature over a wide range.     

Superfluid Couette flow in an enclosed annulus

The Couette configuration of a fluid contained between two rotating concentric cylinders has proved useful to test and validate the HVBK equations which govern the motion of superfluid helium II. We critically review the current understanding of the superfluid Couette problem and compare theory and experiment, distinguishing between the results obtained with infinitely long cylinders and those obtained at small aspect ratio. After discussing some issues which are still unsolved, we point to what should be fruitful directions of further investigation which can be pursued in the Couette configuration.