L. Skrbek

The wind in confined thermal convection

A large-scale circulation velocity, often called the ‘wind’, has been observed in turbulent convection in the Rayleigh–Benard apparatus, which is a closed box with a heated bottom wall. The wind survives even when the dynamical parameter, namely the Rayleigh number, is very large. Over a wide range of time scales greater than its characteristic turnover time, the wind velocity exhibits occasional and irregular reversals without a change in magnitude. We study this feature experimentally in an apparatus of aspect ratio unity, in which the highest attainable Rayleigh number is about 10 16 . A possible physical explanation is attempted.

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 0.60Tc (where Tc 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.Hydrodynamic flow in both classical and quantum fluids can be either laminar or turbulent. To describe the latter, vortices in turbulent flow are modelled with stable vortex filaments. While this is an idealization in classical fluids, vortices are real topologically stable quantized objects in superfluids. Thus superfluid turbulence is thought to hold the key to new understanding on turbulence in general. The fermion superfluid 3He offers further possibilities owing to a large variation in its hydrodynamic characteristics over the experimentally accessible temperatures. While studying the hydrodynamics of the B phase of superfluid 3He, we discovered a sharp transition at 0.60Tc between two regimes, with regular behaviour at high-temperatures and turbulence at low-temperatures. Unlike in classical fluids, this transition is insensitive to velocity and occurs at a temperature where the dissipative vortex damping drops below a critical limit. This discovery resolves the conflict between existing high- and low-temperature measurements in 3He-B: At high temperatures in rotating flow a vortex loop injected into superflow has been observed to expand monotonically to a single rectilinear vortex line, while at very low temperatures a tangled network of quantized vortex lines can be generated in a quiescent bath with a vibrating wire. The solution of this conflict reveals a new intrinsic criterion for the existence of superfluid turbulence.

Developed quantum turbulence and its decaya)

This article is primarily a review of our knowledge of the correspondence between classical and quantum turbulence, though it is interspersed with a few new interpretations. This review is deemed timely because recent work in quantum turbulence promises to provide a better understanding of aspects of classical turbulence, though the two fields of turbulence have similarities as well as differences. We pay a particular attention to the conceptually simplest case of zero temperature limit where quantum turbulence consists of a tangle of quantized vortex line and represents a simple prototype of turbulence. At finite temperature, we anchor ourselves at the level of two-fluid description of the superfluid state—consisting of a normal viscous fluid and a frictionless superfluid—and review much of the available knowledge on quantum turbulence in liquid helium (both He II and 3He-B). We consider counterflows in which the normal and superfluid components flow against each other, as well as co-flows in which the d...

Introduction to quantum turbulence

The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose–Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.

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.

Characteristics of the transition to turbulence in superfluid He4 at low temperatures

A piezoquartz oscillator (tuning fork) immersed in liquid is used to study the kinetic and dissipative processes in He II experimentally. The electrical response of the tuning fork near its resonance frequency is measured with different exciting voltages at temperatures ranging from 0.1Kto4.2K. The measured values of the half-width of the resonance curves made it possible to determine the viscosity of the normal component of He II in a wide temperature range. A maximum of the effective viscosity is found at temperature ∼0.5K; this maximum is due to a transition from the hydrodynamic to the ballistic regime in the phonon gas in He II. It is established that for low velocities of oscillation of the tuning fork the velocities are a linear function of the excitation force; this corresponds to laminar flow of the liquid in the boundary layer near the oscillating surface. The main dissipative process is associated with the viscosity of the normal component. The thickness of the boundary layer near the surface o...

The Nucleation of Superfluid Turbulence at Very Low Temperatures by Flow Through a Grid

Recent experiments by Nichol et al. (cond-mat/0309245 v2) have been concerned with the dynamical behaviour of a grid oscillating in superfluid 4He at a very low temperature, where the normal fluid can be ignored. An interesting enhancement of the effective mass of the grid was observed above a first threshold velocity, without significant increase in damping. Only above a second larger threshold was there a large increase in damping, resulting, we presume, from the generation of turbulence. We show now how the increase in effective mass can be understood in terms of an adiabatic response of the remanent quantized vortices that are knoum to be present, usually, in superfluid helium. Only at the larger threshold is the adiabatic response replaced by a dissipative evolution into a turbulent tangle of vortex lines. We present a semi-quantitative analysis of the experimental results, which suggests strongly that the remanent vortices must take the form of a rather high density of vortex loops attached to the grid. But confirmation of our ideas must await the completion of further experiments and a programme of non-trivial computer simulations.

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.

Decay of counterflow turbulence in superfluid 4He

We summarize recent experiments on thermal counterflow turbulence in superfluid 4He, emphasizing the observation of turbulence in the normal fluid and its effect on the decay process when the heat flux is turned off. We argue that what is observed as turbulence in the normal fluid is a novel form of coupled turbulence in the superfluid and normal components, with injection of energy on the scales of both the (large) channel width and the (small) spacing between quantized vortices. Although an understanding of this coupled turbulence remains challenging, a theory of its decay is developed which accounts for the experimental observations.