Thermal Waves and Heat Transfer Efficiency Enhancement in Harmonically Modulated Turbulent Thermal Convection.

We study turbulent Rayleigh-Bénard convection over four decades of Rayleigh numbers 4×10^{8}

Thermal radiation in Rayleigh-Bénard convection experiments.

An important question in turbulent Rayleigh-Bénard convection (RBC) is the effectiveness of convective heat transport, which is conveniently described via the scaling of the Nusselt number (Nu) with the Rayleigh (Ra) and Prandtl (Pr) numbers. In RBC experiments, the heat supplied to the bottom plate is also partly transferred by thermal radiation. This heat transport channel, acting in parallel with the convective and conductive heat transport channels, is usually considered insignificant and thus neglected. Here we present a detailed analysis of conventional far-field as well as strongly enhanced near-field radiative heat transport occurring in various RBC experiments. A careful inclusion of the radiative transport appreciably changes the Nu=Nu(Ra) scaling inferred in turbulent RBC experiments near ambient temperature utilizing gaseous nitrogen and sulfur hexafluoride as working fluids. On the other hand, neither the conventional far-field radiation nor the strongly enhanced near-field radiative heat transport appreciably affects the heat transport law deduced in cryogenic helium RBC experiments.

Elusive transition to the ultimate regime of turbulent Rayleigh-Bénard convection.

By using cryogenic ^{4}He gas as the working fluid in a cylindrical cell 0.3 m in both height and diameter, we study the influence of non-Oberbeck-Boussinesq (NOB) effects on the heat transfer in turbulent Rayleigh-Bénard convection (RBC). We show that the NOB effects increase the heat transfer efficiency when the top plate temperature closely approaches the saturation vapor curve even far away from the critical point. Viewed in this light, our analysis points to the likelihood that the claim of having observed the transition to Kraichnan's ultimate regime, under nominally similar conditions in the experiments with SF_{6} [Phys. Rev. Lett. 108, 024502 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.024502], is probably an NOB effect and the important issue of the transition to the ultimate state of RBC remains open.

Terahertz wire-grid circular polarizer tuned by lock-in detection method.

We report the design, construction, and testing of a broadband-tunable terahertz circular polarizer, which we developed for our magneto-optical measurements using the far-infrared/THz laser source in the range of 0.25-7.5 THz. We present a thorough analysis of the lock-in amplifier signal generated by using a rotating analyzer with regard to setting the desired state of polarization. The phase-sensitive detection method is applied to a combination of a wire-grid polarizer and a parallel translation mirror providing a tunable retardance. The proposed technique is appropriate not only to free-standing grids but also to those deposited on transparent substrates which may introduce additional non-linear effects. The method is preferred when the distance between the mirror and the grid cannot be exactly determined, but the relative displacements are measured. The device enables switching between left- and right-handed polarization states on a time scale of a few seconds. Practical use of the circular polarizer is demonstrated by directly probing the far infra-red magneto-optical properties of the two-dimensional electron gas on the 458 µm laser line.

Effect of boundary layers asymmetry on heat transfer efficiency in turbulent Rayleigh-Bénard convection at very high Rayleigh numbers [corrected].

The heat transfer efficiency in turbulent Rayleigh-Bénard convection is investigated experimentally, in a cylindrical cell of height 0.3 m, diameter 0.3 m. We show that for Rayleigh numbers 10(12) < or approximately equal to Ra < or approximately equal to 10(15) the Nusselt number closely follows Nu is proportional to Ra(1/3 if the mean temperature of the working fluid-cryogenic helium gas-is measured by small sensors directly inside the cell at about half of its height. In contrast, if the mean temperature is determined in a conventional way, as an arithmetic mean of the bottom and top plate temperatures, the Nu(Ra) is proportional to Ra(γ) displays spurious crossover to higher γ that might be misinterpreted as a transition to the ultimate Kraichnan regime.

Testing the performance of a cryogenic visualization system on thermal counterflow by using hydrogen and deuterium solid tracers.

An experimental apparatus has been designed to analyze by visualization cryogenic flows of liquid (4)He and consequently address unresolved problems of quantum turbulence. The newly implemented flow visualization setup is described and its specific features discussed. Thermal counterflow experiments have been performed and the motion of solid hydrogen and deuterium tracers studied by using the particle tracking velocimetry technique in order to probe the system capabilities. It is shown that the obtained results are consistent with the two-fluid model describing the behavior of superfluid (4)He. A number of technical and fundamental issues, such as particles' aggregation, role of rotating particles in counterflow and evidence of non-Gaussian distribution of tracers' velocities, are also discussed. The apparatus appears to be well-suited to the task of analyzing cryogenic flows and potentially capable of obtaining new results stimulating further understanding of the underlying physics.

Efficiency of heat transfer in turbulent Rayleigh-Bénard convection.

We present an experimental study of turbulent Rayleigh-Bénard convection (RBC) in a cylindrical cell of height 0.3 m, diameter 0.3 m. It is designed to minimize the influence of its structure on the convective flow of cryogenic (4)He gas of Prandtl number Pr≈1, with the aim of resolving existing contradictions in Nusselt (Nu) versus Rayleigh number (Ra) scaling. For 7.2×10(6)≤Ra≤10(11) our data agree with suitably corrected data from similar cryogenic experiments and are consistent with Nu∝Ra(2/7). On approaching Ra≈10(11) our data display a crossover to Nu∝Ra(1/3) that approximately holds up to Ra=4.6×10(13); there is no sign of a transition to the ultimate Kraichnan regime. Differences in Nu(Ra) scaling observed in similar RBC experiments for Ra≥10(11) cannot be explained due to the difference in Pr, but seem to depend also on experimental details.

Helium cryostat for experimental study of natural turbulent convection.

Published experiments on natural turbulent convection in cryogenic (4)He gas show contradictory results in the values of Rayleigh number (Ra) higher than 10(11). This paper describes a new helium cryostat with a cylindrical cell designed for the study of the dependence of the Nusselt number (Nu) on the Rayleigh number (up to Ra approximately 10(15)) in order to help resolve the existing controversy among published experimental results. The main part of the cryostat is a cylindrical convection cell of 300 mm in diameter and up to 300 mm in height. The cell is designed for measurement of heat transfer by natural convection at pressures ranging from 100 Pa to 250 kPa and at temperatures between 4.2 and 12 K. Parasitic heat fluxes into the convection medium are minimized by using thin sidewalls of the bottom and top parts of the cell. The exchangeable central part of the cell enables one to modify the cell geometry.

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.

Steady and decaying flow of He II in a channel with ends blocked by superleaks.

We report a new thermally generated steady-state flow of He II and its decay. An upward superflow through vertical channels of a square cross section with ends blocked by sintered silver superleaks is induced by a fountain pump. On increasing the heat power Q[over ] a vortex-free superflow and, above an intrinsic critical velocity of about 1.5 cm/s, two distinctly different turbulent steady-state flows characterized by the vortex line density L proportional, variantQ[over ];{2} and L proportional, variantQ[over ] are observed using the second sound attenuation technique. When Q[over ] is switched off, after a fast initial decay an exponential decay law is observed. A simple phenomenological model is introduced, capturing the observed features.

Effective kinematic viscosity of turbulent He II.

The temperature dependence of the effective kinematic viscosity of turbulent He II, nu(eff)(T) , is deduced from second sound attenuation data using the late stage of decay of thermally induced counterflow He II turbulence in two channels of square cross section. It is shown to qualitatively agree with the published data for nu(eff)(T) calculated based on experiments on decaying-grid-generated He II turbulence [Niemela, J. Low Temp. Phys. 138, 537 (2005)]. Corrections to these data due to the "sine squared" law that describes attenuation of the second sound wave propagating along an arbitrary direction with respect to the direction of the core of a quantized vortex in turbulent He II are discussed and applied.

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.

Depolarization of decaying counterflow turbulence in He II.

We present experimental evidence backed up by numerical simulations that the steady-state vortex tangle created in He II by heat-transfer counterflow is strongly polarized. When the heater that generates the counterflow turbulence is switched off, the vortex tangle decays, the vortex lines randomize their spatial orientation and the tangle's polarization decreases. The process of depolarization slows down the recovery of the transverse second sound signal which measures the vortex line density; at some values of parameters it even leads to a net decrease of the amplitude of the transverse second sound prior to reaching the universal -32 power temporal law decay typical of classical homogeneous isotropic turbulence in a finite-sized channel.

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.

Experiments on the rapid mechanical expansion of liquid 4He through its superfluid transition.

Phenomena following a rapid mechanical quench of liquid 4He from its normal to its superfluid phase are reported and discussed. The mechanical expansion apparatus is an improved version of that described previously. It uses a double-cell geometry to effect a partial separation of the sample from the convolutions of the bellows that form the outer wall of the cell. Consistent with earlier work, no evidence is found for the production of quantized vortices via the Kibble-Zurek (KZ) mechanism. Although the expansion is complete within 15ms , the second-sound velocity and attenuation continue to increase for a further approximately 60ms ; correspondingly the temperature decreases. Subsequently, the temperature rises again toward its final value as the second-sound velocity and attenuation decrease. It is shown that this unexpected behavior is apparently associated with a large-amplitude second-sound oscillation produced by the expansion, and it is suggested that the observed vortices are created by the normal fluid-superfluid counterflow that constitutes the second-sound wave. If production of large-amplitude second sound is inherent to the mechanical expansion of liquid 4He through the superfluid transition, as appears to be the case for final temperatures more than 3mK from the lambda transition, the phenomenon sets a lower bound on the density of KZ vortices that can be detected in this type of experiment.

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

A systematic experimental investigation of the macroscopic flow properties of extremely pure He II in the zero temperature limit is reported, covering the pressure range 0.3

Flow of He II due to an oscillating grid in the low-temperature limit.

The macroscopic flow properties of pure He II are probed in the limit of zero temperature using an oscillating grid. As the oscillation amplitude passes a first critical threshold, the resonant frequency starts decreasing but the flow remains nondissipative. Beyond a second critical amplitude, the flow undergoes a transition to turbulence and becomes dissipative. Nonlinearity and hysteresis observed between the thresholds are attributed to a boundary layer of quantized vortices.

An intrinsic velocity-independent criterion for superfluid turbulence.

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

Decay of counterflow He II turbulence in a finite channel: possibility of missing links between classical and quantum turbulence.

Decay of He II counterflow turbulence generated by applying a heat pulse to the closed end of a circular channel is investigated using second sound attenuation. Several orders of magnitude of decaying vortex line density display various regimes, starting with the inverse time decay predicted by Vinen towards distinct classical t(-3/2) power law occurring after saturation of the energy containing length scale by the size of the channel. The decaying counterflow turbulence displays a surprisingly close resemblance to recently reported decaying grid turbulence in He II, and both of them appear closely linked to classical grid generated turbulence.