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Workshop on New Experimental Techniques for the Study of Quantum
Turbulence, ICTP, Trieste, June 2005
Introduction and Overview
Joe Vinen
School of Physics and Astronomy
University of Birmingham, UK
Introduction
 Welcome to this workshop which is concerned with experimental techniques
for the study of turbulence in superfluids (“quantum turbulence”).
 The study of turbulence in a classical fluid has been based on many detailed
experimental observations..
 These include:
• simple direct visualization of the flow (Leonardo da Vinci onwards)
• measurement of forces and pressure gradients
• measurement of velocity fields (hot wires; laser Doppler; PIV)
• measurement of correlation functions, energy spectra, etc.
 Role of computer simulations (displacing experimental data?!)
Observations of quantum turbulence
 In contrast, observations on quantum turbulence have been very limited.
• Forces and pressure (temperature) gradients
• Turbulence in superfluid component takes form of irregular configuration
of quantized vortex lines. Much of our knowledge has come from
techniques for measuring the density of these lines (perhaps with some,
but not good, spatial resolution). The classical analogue would be a
measurement of the mean square vorticity, with poor spatial resolution.
• One measurement of pressure fluctuations with fairly good spatial
resolution.
• And that is about all! Little or no direct visualization!
 How much progress could we have expected with classical turbulence with
such limited tools? Given the limited tools, progress in quantum turbulence
has been remarkable, but gaps (known or unknown) exist in our knowledge.
 Role of computer simulations. Crucially important. But many questions
are beyond the power of existing computer simulations (eg whether the
normal fluid is turbulent in thermal counterflow in 4He). And there are still
fundamental uncertainties relating to the way we include reconnections.
Aim of the Workshop
 Hence the purpose of this Workshop: new and improved experimental tools
for quantum turbulence. Review existing tools and look to develop new tools.
 More detailed knowledge will allow us to interact more strongly with our
colleagues in classical fluid mechanics. Need for more sophisticated
measurements.
 No proceedings, but hopefully a Report, which can be used in planning our
work and in seeking support for it.
Types of quantum turbulence
 How is turbulence nucleated and how does it build up in its early stages?
 Characteristics of fully-developed turbulence: analogues of Richardson
cascades, Kolmogorov dissipation lengths, intermittency, coherent
structures, etc.
 Nucleation and early build-up tends to involve small lengths of vortex so is
especially amenable to computer simulation. The role of computer
simulation, including its power and limitations, will be discussed at the end
of this Workshop by Tsubota.
Review of present and future techniques
 In introducing these techniques let us focus initially on fully-developed
turbulence in a steady state or quasi-steady state.
 Length scales and time scales:
• As in classical turbulence there is likely to be a wide range of scales.
• From the size of the obstacle or channel giving rise to the turbulence to
the (small) scale on which dissipation occurs.
• The smallest scale can be very small. Eg: for turbulence in 4He above
1K in which the energy-containing eddies have size 1 cm and
characteristic velocity 1 cm s-1, the smallest scale is about 30 microns;
the time scale ranges from 1 s to a few milliseconds. Below 1K the need
for a Kelvin wave cascade to dissipate energy may take the smallest
scale to 10 nm. Ideally our techniques ought to cover these ranges.
 Can we measure velocity correlation functions, which play an important role
in classical turbulence (structure functions)? We could derive energy spectra
from them and look for deviations from Kolmogorov scaling (higher-order SFs).
Visualizing the flow
 One should not underestimate the importance of visualizing the flow.
 Kolmogorov scaling suggests that turbulence is very random on small
scales. Measurements of velocity correlations etc are not obviously
inconsistent with this view. But looking at a classical turbulent flow reveals
the existence of “coherent structures” (classical vortex filaments). What has
happened to these structures in quantum turbulence?
 Visualizing the flow usually involves tracer particles. Their motion can be
followed by using Laser Doppler Velocimetry (LDV) or Particle Image
Velocimetry (PIV). We shall discuss the extent to which we can use
(especially) PIV in a superfluid. Two problems: choice of particle (neutrally
buoyant); interpretation of results (more than one velocity field).
Experiments will be discussed by Van Sciver and Bewley; interpretation by
Barenghi (not straightforward!!). We may wish to discuss also LDV.
 Use of “unconventional” tracer particles: such as neutral triplet-state He2
molecules; I will discuss some ideas originating from McKinsey at Yale.
 Lucas will describe his shadowgraph technique for visualizing convective
flow in 3He-4He mixtures, and its possible applications to other types of flow.
Localized probes
 We shall wish to discuss probes (other than PIV and LDV) that measure
local properties (such as pressure, velocity). Remember that ideally we need
a spatial resolution of at least 30 microns and a frequency response to at
least 1 kHz.
 Hot wire anemometers do not work in 4He owing to the high thermal
conductivity. Could they work in 3He?
 A pressure transducer with a spatial resolution of about 1 mm and good
frequency response was used in an important experiment by Maurer and
Tabeling. Ihas will discuss the development of smaller pressure transducers
based on nano-fabrication techniques.
 In the Maurer-Tabeling experiment the pressure transducer was exposed to
a steady “biasing” flow, giving two advantages: the pressure fluctuations
then measure the frequency spectrum of v2; and the transition from a
frequency spectrum to a spatial (energy) spectrum is then easy.
 A biasing flow is generally difficult to arrange, so we need to discuss the
interpretation of pressure fluctuations in its absence.
Second Sound and NMR
 Measurement of the attenuation of second sound has been extremely
important in the study of quantum turbulence. Mostly it has been used to
measure average vortex line densities over large volumes, and it can be
sensitive to very small line densities.
 We need to assess the extent to which second sound transducers can be
developed with significant spatial resolution, while retaining high sensitivity,
to look at fluctuations in line density. We shall have presentations by Skrbek
and by Roche. Skrbek will focus on the high sensitivity. Roche will describe
a development in which a spatial resolution of 300 microns has been
achieved.
 Second sound does not propagate in 3He. However, at least at fairly high
temperatures NMR signals can then be used to measure vortex densities,
with very high sensitivity. Details will be described by Finne, who will
mention the application to some very interesting studies in Helsinki of the
nucleation of turbulence in rotating 3He-B..
Very Low Temperatures
 There is much interest in quantum turbulence in 4He and 3He-B at
temperatures where the density of normal fluid is negligible. The search for
appropriate experimental techniques for this temperature range poses major
problems. (Second sound does not propagate even in 4He at low temps.)
 Ion trapping can in principle measure line densities, but there are probably
major problems; capture cross-sections are not yet known and may be very
small. Golov will report on the present situation. (Associated simulations.)
 I will report on the possibility of using bubble states formed from triplet state
He2 molecules, which may prove more powerful than the use of ions.
 Miniature pressure sensors may be useful (Ihas), but we need to know
whether they can have adequate sensitivity for the study of decaying
turbulence.
Very Low Temperatures (cond)
 At very low temperatures the thermal energy in a superfluid can be very
small, especially in 4He. This means that turbulent energies can be
comparable with the thermal energy (Barenghi & Samuels for the case of a
random vortex tangle).
 Two consequencies:
• Decay of turbulence can be monitored by observing rise in temperature
(good). See my later discussion.
• Continuous maintenance of steady-state turbulence is impossible
(bad, because gain in sensitivity in a transducer from time-averaging
is ruled out).
 Andreev reflection of thermal quasi-particles in 3He-B by turbulent velocity
fields. Fisher will discuss the extent to which he can use this new technique
to make quantitative measurements of vortex densities and the spatial
distribution of vortices in 3He-B at very low temperatures. .
Nucleation and initial build-up of quantum turbulence
 I have tended to focus implicitly on fully-developed turbulence, where
comparison with classical turbulence is perhaps most straightforward.
 But there are many interesting questions about the nucleation and initial
build-up of quantum turbulence.
 Existing studies here have tended to rely on rather simple measurements
(critical velocities; vortex line densities), combined with extensive computer
simulations to see whether models can be developed to account for these
(rather crude) observations. More detailed experimental evidence would be
valuable, and this must come from techniques that allow observation of
(weak) turbulent regimes that are neither homogeneous nor in a steady state.
The Andreev reflection technique has recently produced some fascinating
evidence about the generation of turbulence by an oscillating grid in 3He-B,
and we look forward to hearing more from Fisher and discussing whether the
ideas may be more widely applicable.
So let us start work.