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 $0.7<Pr<21$ and for the full range of soft and hard turbulences, up to Rayleigh number $Ra\simeq 10^{11}$. 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 $diameter/height=0.5$. The effective heat transfer $Nu(Ra,Pr)$ 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 $Nu(Ra)$ dependence exhibits a bimodality of the flow with $4-7$ difference in $Nu$ for given $Ra$ and $Pr$. Second, a systematic study of the side-wall influence reveals a measurable effect on the heat transfer. Third, the $Nu(Pr)$ dependence is very small or null : the absolute value of the average logarithmic slope $(dlnNu/dlnPr)_{Ra}$ is smaller than 0.03 in our range of $Pr$, 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

Fermi liquid theory of ultra-cold trapped Fermi gases: Implications for Pseudogap Physics and Other Strongly Correlated Phases

We show how Fermi liquid theory can be applied to ultra-cold Fermi gases, thereby expanding their "simulation" capabilities to a class of problems of interest to multiple physics sub-disciplines. We introduce procedures for measuring and calculating position dependent Landau parameters. This lays the ground work for addressing important controversial issues: (i) the suggestion that thermodynamically, the normal state of a unitary gas is indistinguishable from a Fermi liquid (ii) that a fermionic system with strong repulsive contact interactions is associated with either ferromagnetism or localization; this relates as well to $^3$He and its p-wave superfluidity.Comment: 4 pages, 2 figures, revised versio

Unified Multifractal Description of Velocity Increments Statistics in Turbulence: Intermittency and Skewness

The phenomenology of velocity statistics in turbulent flows, up to now, relates to different models dealing with either signed or unsigned longitudinal velocity increments, with either inertial or dissipative fluctuations. In this paper, we are concerned with the complete probability density function (PDF) of signed longitudinal increments at all scales. First, we focus on the symmetric part of the PDFs, taking into account the observed departure from scale invariance induced by dissipation effects. The analysis is then extended to the asymmetric part of the PDFs, with the specific goal to predict the skewness of the velocity derivatives. It opens the route to the complete description of all measurable quantities, for any Reynolds number, and various experimental conditions. This description is based on a single universal parameter function D(h) and a universal constant R*.Comment: 13 pages, 3 figures, Extended version, Publishe

Spin waves in quasi-equilibrium spin systems

Using the Landau Fermi liquid theory we have discovered a new regime for the propagation of spin waves in a quasi-equilibrium spin systems. We have determined the dispersion relation for the transverse spin waves and found that one of the modes is gapless. The gapless mode corresponds to the precessional mode of the magnetization in a paramagnetic system in the absence of an external magnetic field. One of the other modes is gapped which is associated with the precession of the spin current around the internal field. The gapless mode has a quadratic dispersion leading to some interesting thermodynamic properties including a $T^{3/2}$ contribution to the specific heat. We also show that these modes make significant contributions to the dynamic structure function.Comment: 4 pages, 3 figure

From turbulence to financial time series

We develop a framework especially suited to the autocorrelation properties observed in financial times series, by borrowing from the physical picture of turbulence. The success of our approach as applied to high frequency foreign exchange data is demonstrated by the overlap of the curves in Figure (1), since we are able to provide an analytical derivation of the relative sizes of the quantities depicted. These quantities include departures from Gaussian probability density functions and various two and three-point autocorrelation functions.Comment: 10 pages, 1 figure, LaTeX, version to appear in Physica

Lagrangian temperature, velocity and local heat flux measurement in Rayleigh-Benard convection

We have developed a small, neutrally buoyant, wireless temperature sensor. Using a camera for optical tracking, we obtain simultaneous measurements of position and temperature of the sensor as it is carried along by the flow in Rayleigh-B\'enard convection, at $Ra \sim 10^{10}$. We report on statistics of temperature, velocity, and heat transport in turbulent thermal convection. The motion of the sensor particle exhibits dynamics close to that of Lagrangian tracers in hydrodynamic turbulence. We also quantify heat transport in plumes, revealing self-similarity and extreme variations from plume to plume.Comment: 4 page

Lognormal scale invariant random measures

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a by product, we also obtain an explicit characterization of the covariance structure of these measures. We also prove that qualitative properties such as long-range independence or isotropy can be read off the equation.Comment: 31 pages; Probability Theory and Related Fields (2012) electronic versio

Asymptotic behaviour of the Rayleigh--Taylor instability

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin & Williams\cite{clavin} for which we give a simplified demonstration. In particular we observe that the spike's curvature evolves like $t^3$ while the overshoot in acceleration shows a good agreement with the suggested $1/t^5$ law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.Comment: 4 pages, 6 figure

Extraction of Plumes in Turbulent Thermal Convection

We present a scheme to extract information about plumes, a prominent coherent structure in turbulent thermal convection, from simultaneous local velocity and temperature measurements. Using this scheme, we study the temperature dependence of the plume velocity and understand the results using the equations of motion. We further obtain the average local heat flux in the vertical direction at the cell center. Our result shows that heat is not mainly transported through the central region but instead through the regions near the sidewalls of the convection cell.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Effects of electromagnetic waves on the electrical properties of contacts between grains

A DC electrical current is injected through a chain of metallic beads. The electrical resistances of each bead-bead contacts are measured. At low current, the distribution of these resistances is large and log-normal. At high enough current, the resistance distribution becomes sharp and Gaussian due to the creation of microweldings between some beads. The action of nearby electromagnetic waves (sparks) on the electrical conductivity of the chain is also studied. The spark effect is to lower the resistance values of the more resistive contacts, the best conductive ones remaining unaffected by the spark production. The spark is able to induce through the chain a current enough to create microweldings between some beads. This explains why the electrical resistance of a granular medium is so sensitive to the electromagnetic waves produced in its vicinity.Comment: 4 pages, 5 figure