5,997 research outputs found
Applicability of Boussinesq approximation in a turbulent fluid with constant properties
The equations of motion describing buoyant fluids are often simplified using
a set of approximations proposed by J. Boussinesq one century ago. To resume,
they consist in assuming constant fluid properties, incompressibility and
conservation of calories during heat transport. Assuming fulfilment of the
first requirement (constant fluid properties), we derive a set of 4 criteria
for assessing the validity of the two other requirements in turbulent
Rayleigh-B\'enard convection. The first criterion simply
results from the incompressibility condition in the thermal boundary layer
( and are the thermal expansion coefficient and the
temperature difference driving the flow). The 3 other criteria are proportional
or quadratic with the density stratification or, equivalently with the
temperature difference resulting from the adiabatic gradient across the cell
. Numerical evaluations with air, water and cryogenic helium show
that most laboratory experiments are free from such Boussinesq violation as
long as the first criterion is fulfilled. In ultra high Rayleigh numbers
() experiments in He, one of the stratification criteria, scaling
with , could be violated. This criterion garanties that
pressure fluctuations have a negligible influence both on the density variation
and on the heat transfer equation through compression/expansion cycles.
Extrapolation to higher suggests that strong violation of Boussinesq
approximation could occur in atmospheric convection.Comment: Submitted to Phys.Fluids (oct 2007
Shot-noise statistics in diffusive conductors
We study the full probability distribution of the charge transmitted through
a mesoscopic diffusive conductor during a measurement time T. We have
considered a semi-classical model, with an exclusion principle in a discretized
single-particle phase-space. In the large T limit, numerical simulations show a
universal probability distribution which agrees very well with the quantum
mechanical prediction of Lee, Levitov and Yakovets [PRB {51} 4079 (1995)] for
the charge counting statistics. Special attention is given to its third
cumulant, including an analysis of finite size effects and of some experimental
constraints for its accurate measurement.Comment: Submitted to Eur. Phys. J. B (Jan. 2002
Vortex spectrum in superfluid turbulence: interpretation of a recent experiment
We discuss a recent experiment in which the spectrum of the vortex line
density fluctuations has been measured in superfluid turbulence. The observed
frequency dependence of the spectrum, , disagrees with classical
vorticity spectra if, following the literature, the vortex line density is
interpreted as a measure of the vorticity or enstrophy. We argue that the
disagrement is solved if the vortex line density field is decomposed into a
polarised field (which carries most of the energy) and an isotropic field
(which is responsible for the spectrum).Comment: Submitted for publication
http://crtbt.grenoble.cnrs.fr/helio/GROUP/infa.html
http://www.mas.ncl.ac.uk/~ncfb
Quantum turbulence at finite temperature: the two-fluids cascade
To model isotropic homogeneous quantum turbulence in superfluid helium, we
have performed Direct Numerical Simulations (DNS) of two fluids (the normal
fluid and the superfluid) coupled by mutual friction. We have found evidence of
strong locking of superfluid and normal fluid along the turbulent cascade, from
the large scale structures where only one fluid is forced down to the vorticity
structures at small scales. We have determined the residual slip velocity
between the two fluids, and, for each fluid, the relative balance of inertial,
viscous and friction forces along the scales. Our calculations show that the
classical relation between energy injection and dissipation scale is not valid
in quantum turbulence, but we have been able to derive a temperature--dependent
superfluid analogous relation. Finally, we discuss our DNS results in terms of
the current understanding of quantum turbulence, including the value of the
effective kinematic viscosity
Phase space polarization and the topological string: a case study
We review and elaborate on our discussion in hep-th/0606112 on the interplay
between the target space and the worldsheet description of the open topological
string partition function, for the example of the conifold. We discuss the
appropriate phase space and canonical form for the system. We find a map
between choices of polarization and the worldsheet description, based on which
we study the behavior of the partition function under canonical
transformations.Comment: 18 pages, invited review for MPL
Heat Transfer in Turbulent Rayleigh-Benard Convection below the Ultimate Regime
A Rayleigh-B\'enard cell has been designed to explore the Prandtl (Pr)
dependence of turbulent convection in the cross-over range and for
the full range of soft and hard turbulences, up to Rayleigh number . The set-up benefits from the favourable characteristics of cryogenic
helium-4 in fluid mechanics, in-situ fluid property measurements, and special
care on thermometry and calorimetric instrumentation. The cell is cylindrical
with . The effective heat transfer has been
measured with unprecedented accuracy for cryogenic turbulent convection
experiments in this range of Rayleigh numbers. Spin-off of this study include
improved fits of helium thermodynamics and viscosity properties. Three main
results were found. First the dependence exhibits a bimodality of the
flow with difference in for given and . Second, a
systematic study of the side-wall influence reveals a measurable effect on the
heat transfer. Third, the dependence is very small or null : the
absolute value of the average logarithmic slope is smaller
than 0.03 in our range of , which allows to disciminate between
contradictory experiments [Ashkenazi \textit{et al.}, Phys. Rev.Lett. 83:3641
(1999)][Ahlers \textit{et al.}, Phys.Rev.Lett. 86:3320 (2001)].Comment: submitted for publication to JLTP (august 2003
Mesoscale Equipartition of kinetic energy in Quantum Turbulence
The turbulence of superfluid helium is investigated numerically at finite
temperature. Direct numerical simulations are performed with a "truncated HVBK"
model, which combines the continuous description of the
Hall-Vinen-Bekeravich-Khalatnikov equations with the additional constraint that
this continuous description cannot extend beyond a quantum length scale
associated with the mean spacing between individual superfluid vortices. A good
agreement is found with experimental measurements of the vortex density.
Besides, by varying the turbulence intensity only, it is observed that the
inter-vortex spacing varies with the Reynolds number as , like the
viscous length scale in classical turbulence. In the high temperature limit,
Kolmogorov's inertial cascade is recovered, as expected from previous numerical
and experimental studies. As the temperature decreases, the inertial cascade
remains present at large scales while, at small scales, the system evolves
towards a statistical equipartition of kinetic energy among spectral modes,
with a characteristic velocity spectrum. The accumulation of superfluid
excitations on a range of mesoscales enables the superfluid to keep dissipating
kinetic energy through mutual friction with the residual normal fluid, although
the later becomes rare at low temperature. It is found that most of the
superfluid vorticity can concentrate on these mesoscales at low temperature,
while it is concentrated in the inertial range at higher temperature. This
observation should have consequences on the interpretation of decaying
turbulence experiments, which are often based on vortex line density
measurements.Comment: 6 pages, 5 figure
Kolmogorov cascade and equipartition of kinetic energy in numerical simulation of Superfluid turbulence
International audienceThe turbulence of a superfluid is investigated by direct numerical simulations at finite temperature and high Reynolds numbers using the continuous model. The superfluid component is described by the Euler equation while the normal fluid component is described by the Navier-Stokes equation, both being coupled by mutual friction. In the high temperature limit, the Kolmogorov cascade is recovered, as expected from previous numerical and experimental studies. As the temperature decreases, the Kolmogorov cascade remains present at large scales while, at small scales, the system evolves towards a statistical equipartition of kinetic energy among spectral modes
Vortex density spectrum of quantum turbulence
The fluctuations of the vortex density in a turbulent quantum fluid are
deduced from local second-sound attenuation measurements. These measurements
are performed with a micromachined open-cavity resonator inserted across a flow
of turbulent He-II near 1.6 K. The power spectrum of the measured vortex line
density is compatible with a (-5/3) power law. The physical interpretation,
still open, is discussed.Comment: Submitted to Europhys. Let
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