Experimental investigation of the macroscopic flow of He II due to an oscillating grid in the zero temperature limit

Oscillating-grid experiments in water and superfluid helium

Passing a fluid through a grid is a well-known mechanism used to study the properties of turbulence. Oscillating a horizontal grid vertically in a tank has also been used extensively and is considered to be a source of almost homogenous isotropic turbulence. When the oscillating grid is turned on a turbulent flow is induced. A front translates into the experimental tank, behind which the flow is highly turbulent. Long predicted that the growth of such a front would grow diffusively as the square root of time (i.e., d ∼ sqrt[t]) and Dickinson and Long presented experimental evidence for the diffusive result at a low mesh Reynolds number of 555. This paper revisits these experiments and attempts a set of two models for the advancing front in both square and round tanks. We do not observe significant differences between runs in square and round tanks. The experiments in water reach mesh Reynolds numbers of order 30000. Using some data from superfluid helium experiments we are able to explore mesh Reynolds numbers to about 43000. We find the power law for the advancing front decreases weakly with the mesh Reynolds number. Using a very long tank we find that the turbulent front stops completely at a certain depth and attempt a simple explanation for that behavior. We study the propagation of the turbulent front into tubes of different diameters inserted into the main tank. We show that these tubes exclude wavelengths much larger than the tube diameter. We explore the variation of the position of the steady-state boundary H on tube diameter D and find that H = cD with c ∼ 2. We suggest this may be explained by saturation of the energy-containing length scale ℓ(e). We also report on the effect of plugging up just one hole of the grid. Finally, we recall some earlier oscillating grid experiments in superfluid (4)He in the light of the present results.

Transition from laminar to turbulent drag in flow due to a vibrating quartz fork

Flow due to a commercially available vibrating quartz fork is studied in gaseous helium, He I and He II, over a wide range of temperatures and pressures. On increasing the driving force applied to the fork, the drag changes in character from laminar (characterized by a linear drive vs velocity dependence) to turbulent (characterized by a quadratic drive vs velocity dependence). We characterize this transition by a critical Reynolds number Recrdelta=Ucrdelta/nu, where Ucr is the critical velocity, nu stands for the kinematic viscosity, delta=sqrt[2nu/omega] is the viscous penetration depth, and omega is the angular frequency of oscillations. We have experimentally verified that the corresponding scaling Ucr proportional, sqrt[nuomega] holds in a classical viscous fluid over two decades of nu.

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.

Classical rotational inertia of solid 4He

The observation of reduced rotational inertia in a cell containing solid 4He has been interpreted as evidence for superfluidity of the solid. We propose an alternative explanation: slippage of the solid, due to grain boundary premelting between the solid and dense adsorbed layers at the container wall. We calculate the range of film thickness, and determine the viscosity that will account for the missing rotational inertia. Grain boundary premelting also explains inertial anomalies in an earlier study of solid helium in porous glass and indicates that the liquid is partially superfluid.