Dissipation of Quasiclassical Turbulence in Superfluid

We compare the decay of turbulence in superfluid ^{4}He produced by a moving grid to the decay of turbulence created by either impulsive spin-down to rest or by intense ion injection. In all cases, the vortex line density L decays at late time t as L∝t^{-3/2}. At temperatures above 0.8 K, all methods result in the same rate of decay. Below 0.8 K, the spin-down turbulence maintains initial rotation and decays slower than grid turbulence and ion-jet turbulence. This may be due to a decoupling of the large-scale superfluid flow from the normal component at low temperatures, which changes its effective boundary condition from no-slip to slip.

Producing and imaging a thin line of He*2 molecular tracers in helium-4.

Cryogenic helium-4 has long been recognized as a useful material in fluids research. The unique properties of helium-4 in the gaseous phase and the normal liquid phase allow for the generation of turbulent flows with exceptionally high Reynolds and Rayleigh numbers. In the superfluid phase, helium-4 exhibits two-fluid hydrodynamics and possesses fascinating properties due to its quantum nature. However, studying the flows in helium-4 has been very challenging largely due to the lack of effective visualization and velocimetry techniques. In this article, we discuss the development of novel instrumentation for flow-visualization in helium based on the generation and imaging of thin lines of metastable He*2 tracer molecules. These molecular tracers are created via femtosecond-laser field-ionization of helium atoms and can be imaged using a laser-induced fluorescence technique. By observing the displacement and distortion of the tracer lines in helium, quantitative information about the flow field can be extracted. We present experimental results in the study of thermal counterflow in superfluid helium that validate the concept of this technique. We also discuss anticipated future developments of this powerful visualization technique.

Excimers He2* as tracers of quantum turbulence in 4He in the t = 0 limit.

We have studied the interaction of metastable 4He2* excimer molecules with quantized vortices in superfluid 4He in the zero temperature limit. The vortices were generated by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be 96±6 nm at a pressure of 0.1 bar and 27±5 nm at 5.0 bar. We have also demonstrated that a moving tangle of vortices can carry the molecules through the superfluid helium.

Experiments relating to the flow induced by a vibrating quartz tuning fork and similar structures in a classical fluid.

We report on an experimental study of the behavior of a number of commercially available quartz tuning forks oscillating in a classical cryogenic fluid, in the form of either liquid helium I or gaseous helium, extending our previous studies [M. Blazkova Phys. Rev. E 75, 025302 (2007)]. Measurements of the damping of the oscillations allowed us to deduce the drag on the prong of a fork, as a function of the velocity with which the prong moves, for various sizes of fork and various oscillation frequencies. Transitions to turbulent flow have been identified, and the dependence of the critical velocity, expressed as a dimensionless critical Keulegan-Carpenter number, on the dimensionless Stokes number has been established. These measurements have not allowed us to visualize the flow, so we have carried out visualization experiments with oscillating rods in water, the rod dimensions, and the frequencies of oscillation, being chosen so that the relevant dimensionless parameters are similar to those for the prongs of the forks. Some information about the nature of the instability that leads to turbulence has been obtained in this way, and the results for the critical Keulegan-Carpenter number for the rods in water have been compared with values for the tuning forks in a cryogenic fluid.

Visualization study of counterflow in superfluid 4He using metastable helium molecules.

Heat is transferred in superfluid 4He via a process known as thermal counterflow. It has been known for many years that above a critical heat current the superfluid component in this counterflow becomes turbulent. It has been suspected that the normal-fluid component may become turbulent as well, but experimental verification is difficult without a technique for visualizing the flow. Here we report a series of visualization studies on the normal-fluid component in a thermal counterflow performed by imaging the motion of seeded metastable helium molecules using a laser-induced-fluorescence technique. We present evidence that the flow of the normal fluid is indeed turbulent at relatively large velocities. Thermal counterflow in which both components are turbulent presents us with a theoretically challenging type of turbulent behavior that is new to physics.

An introduction to quantum turbulence.

This paper provides a brief introduction to quantum turbulence in simple superfluids, in which the required rotational motion in the superfluid component is due entirely to the topological defects that are identified as quantized vortices. Particular emphasis is placed on the basic dynamical behaviour of the quantized vortices and on turbulent decay mechanisms at a very low temperature. There are possible analogies with the behaviour of cosmic strings.

Dissipation of quantum turbulence in the zero temperature limit.

Turbulence, produced by an impulsive spin down from angular velocity Omega to rest of a cube-shaped container, is investigated in superfluid 4He at temperatures 0.08 K-1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Homogeneous turbulence develops after time t approximately 20/Omega and decays as L proportional, t-3/2. The corresponding energy flux =nu'(kappaL)2 proportional, t-3 is characteristic of quasiclassical turbulence at high Re with a saturated energy-containing length. The effective kinematic viscosity in T=0 limit is nu'=0.003kappa, where kappa=10(-3) cm2 s(-1) is the circulation quantum.

Experimental investigation of the dynamics of a vibrating grid in superfluid 4He over a range of temperatures and pressures.

In an earlier paper [Nichol, Phys. Rev. E, 70, 056307 (2004)] some of the present authors presented the results of an experimental study of the dynamics of a stretched grid driven into vibration at or near its resonant frequency in isotopically pure superfluid 4He over a range of pressures at a very low temperature, where the density of normal fluid is negligible. In this paper we present the results of a similar study, based on a different grid, but now including the temperature range where the normal fluid density is no longer insignificant. The new grid is very similar to the old one except for a small difference in the character of its surface roughness. In many respects the results at low temperature are similar to those for the old grid. At low amplitudes the results are somewhat history dependent, but in essence there is no damping greater than that in vacuo. At a critical amplitude corresponding to a velocity of about 50 mms(-1) there is a sudden and large increase in damping, which can be attributed to the generation of new vortex lines. Strange shifts in the resonant frequency at intermediate amplitudes observed with the old grid are no longer seen, however they must therefore have been associated with the different surface roughness, or perhaps were due simply to some artifact of the old grid, the details of which we are currently unable to determine. With the new grid we have studied both the damping at low amplitudes due to excitations of the normal fluid, and the dependence of the supercritical damping on temperature. We present evidence that in helium at low amplitudes there may be some enhancement in the effective mass of the grid in addition to that associated with potential flow of the helium. In some circumstances small satellite resonances are seen near the main fundamental grid resonance, which are attributed to coupling to some other oscillatory system within the experimental cell.

Kelvin-wave cascade on a vortex in superfluid 4He at a very low temperature.

A study by computer simulation is reported of the behavior of a quantized vortex line at a very low temperature when there is continuous excitation of low-frequency Kelvin waves. There is no dissipation except by phonon radiation at a very high frequency. It is shown that nonlinear coupling leads to a net flow of energy to higher wave numbers and to the development of a simple spectrum of Kelvin waves that is insensitive to the strength and frequency of the exciting drive. The results are likely to be relevant to the decay of turbulence in superfluid 4He at very low temperatures.