Bernard Castaing

Comparison between rough and smooth plates within the same Rayleigh–Bénard cell

In a Rayleigh–Benard cell at high Rayleigh number, the bulk temperature is nearly uniform. The mean temperature gradient differs from zero only in the thin boundary layers close to the plates. Measuring this bulk temperature allows to separately determine the thermal impedance of each plate. In this work, the bottom plate is rough and the top plate is smooth; both interact with the same bulk flow. We compare them and address in particular the question whether the influence of roughness goes through a modification of the bulk flow.

A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows

Abstract A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian) velocity increments. The universal nature of the intermittency phenomenon as observed in experimental measurements and numerical simulations is shown to be fully taken into account by the multiscale picture proposed by the multifractal formalism, and its extensions to the dissipative scales and to the Lagrangian framework. The article is devoted to the presentation of these arguments and to their comparisons against empirical data. In particular, explicit predictions of the statistics, such as probability density functions and high order moments, of the velocity gradients and acceleration are derived. In the Eulerian framework, at a given Reynolds number, they are shown to depend on a single parameter function called the singularity spectrum and to a universal constant governing the transition between the inertial and dissipative ranges. The Lagrangian singularity spectrum compares well with its Eulerian counterpart by a transformation based on incompressibility, homogeneity and isotropy and the remaining constant is shown to be difficult to estimate on empirical data. It is finally underlined the limitations of the increment to quantify accurately the singular nature of Lagrangian velocity. This is confirmed using higher order increments unbiased by the presence of linear trends, as they are observed on velocity along a trajectory.

Heat convection in a vertical channel : Plumes versus turbulent diffusion

Following a previous study [Gibert et al., Phys. Rev. Lett. 96, 084501 (2006)], convective heat transfer in a vertical channel of moderate dimensions follows purely inertial laws. It would be therefore a good model for convective flows of stars and ocean. Here we report new measurements on this system. We use an intrinsic length in the definition of the characteristic Rayleigh and Reynolds numbers. We explicit the relation between this intrinsic length and the thermal correlation length. Using particle imaging velocimetry, we show that the flow undergoes irregular reversals. We measure the average velocity profiles and the Reynolds stress tensor components. The momentum flux toward the vertical walls seems negligible compared to the shear turbulent stress. A mixing length theory seems adequate to describe the horizontal turbulent heat and momentum fluxes, but fails for the vertical ones. We propose a naive model for vertical heat transport inspired by the Knudsen regime in gases.

Static Spectroscopy of a Dense Superfluid

Dense Bose superfluids, as HeII, differ from dilute ones by the existence of a roton minimum in their excitation spectrum. It is known that this roton minimum is qualitatively responsible for density oscillations close to any singularity, such as vortex cores, or close to solid boundaries. We show that the period of these oscillations, and their exponential decrease with the distance to the singularity, are fully determined by the position and the width of the roton minimum. Only an overall amplitude factor and a phase shift are shown to depend on the details of the interaction potential. Reciprocally, it allows for determining the characteristics of this roton minimum from static “observations” of a disturbed ground state, in cases where the dynamics is not easily accessible. We focus on the vortex example. Our analysis further shows why the energy of these oscillations is negligible compared to the kinetic energy, which limits their influence on the vortex dynamics, except for high curvatures.

Rough horizontal plates: heat transfer and hysteresis

To investigate the influence of a rough-wall boundary layer on turbulent heat transport, an experiment of high-Rayleigh convection in water is carried out in a Rayleigh-Benard cell with a rough lower plate and a smooth upper plate. A transition in the heat transport is observed when the thermal boundary layer thickness becomes comparable to or smaller than the roughness height. Besides, at larger Rayleigh numbers than the threshold value, heat transport is found to be increased up to 60 %. This enhancement cannot be explained simply by an increase in the contact area of the rough surface since the contact area is increased only by a factor of 40 %. Finally, a simple model is proposed to explain the enhanced heat transport.

Phenomenological relation between the Kolmogorov constant and the skewness in turbulence

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. Based on experimental longitudinal velocity profiles, we show that velocity statistics can be completely understood phenomenologically with the help of two sets of parameters, a parameter function D(h), well known in the multifractal formalism as the singularity spectrum (in the inviscid limit) and an additional universal constant R*. (i.e. independent on the Reynolds number and the geometry of the flow). The measurable parameter function D(h) is well known in the turbulence literature [1]. It encodes several crucial inertial range informations [1] such as K41 predictions (namely, the ‘-5/3” law of the power spectrum) and intermittent corrections. Furthermore, it allows a quantitative prediction of the behavior of the even order structure functions in the intermediate and far-dissipative ranges (see for instance [2]).