Two-dimensionalization of the flow driven by a slowly rotating impeller in a rapidly rotating fluid

We characterize the two-dimensionalization process in the turbulent flow produced by an impeller rotating at a rate $\omega$ in a fluid rotating at a rate $\Omega$ around the same axis for Rossby number $Ro=\omega/\Omega$ down to $10^{-2}$. The flow can be described as the superposition of a large-scale vertically invariant global rotation and small-scale shear layers detached from the impeller blades. As $Ro$ decreases, the large-scale flow is subjected to azimuthal modulations. In this regime, the shear layers can be described in terms of wakes of inertial waves traveling with the blades, originating from the velocity difference between the non-axisymmetric large-scale flow and the blade rotation. The wakes are well defined and stable at low Rossby number, but they become disordered at $Ro$ of order of 1. This experiment provides insight into the route towards pure two-dimensionalization induced by a background rotation for flows driven by a non-axisymmetric rotating forcing.Comment: Accepted for publication in Physical Review Fluid

Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid

We analyze theoretically and experimentally the far-field viscous decay of a two-dimensional inertial wave beam emitted by a harmonic line source in a rotating fluid. By identifying the relevant conserved quantities along the wave beam, we show how the beam structure and decay exponent are governed by the multipole order of the source. Two wavemakers are considered experimentally, a pulsating and an oscillating cylinder, aiming to produce a monopole and a dipole source, respectively. The relevant conserved quantity which discriminates between these two sources is the instantaneous flowrate along the wave beam, which is non-zero for the monopole and zero for the dipole. For each source the beam structure and decay exponent, measured using particle image velocimetry, are in good agreement with the predictions

Disentangling inertial waves from eddy turbulence in a forced rotating turbulence experiment

We present a spatio-temporal analysis of a statistically stationary rotating turbulence experiment, aiming to extract a signature of inertial waves, and to determine the scales and frequencies at which they can be detected. The analysis uses two-point spatial correlations of the temporal Fourier transform of velocity fields obtained from time-resolved stereoscopic particle image velocimetry measurements in the rotating frame. We quantify the degree of anisotropy of turbulence as a function of frequency and spatial scale. We show that this space-time-dependent anisotropy is well described by the dispersion relation of linear inertial waves at large scale, while smaller scales are dominated by the sweeping of the waves by fluid motion at larger scales. This sweeping effect is mostly due to the low-frequency quasi-two-dimensional component of the turbulent flow, a prominent feature of our experiment which is not accounted for by wave turbulence theory. These results question the relevance of this theory for rotating turbulence at the moderate Rossby numbers accessible in laboratory experiments, which are relevant to most geophysical and astrophysical flows

Turbulent drag in a rotating frame

What is the turbulent drag force experienced by an object moving in a rotating fluid? This open and fundamental question can be addressed by measuring the torque needed to drive an impeller at constant angular velocity $\omega$ in a water tank mounted on a platform rotating at a rate $\Omega$. We report a dramatic reduction in drag as $\Omega$ increases, down to values as low as $12$\% of the non-rotating drag. At small Rossby number $Ro = \omega/\Omega$, the decrease in drag coefficient $K$ follows the approximate scaling law $K \sim Ro$, which is predicted in the framework of nonlinear inertial wave interactions and weak-turbulence theory. However, stereoscopic particle image velocimetry measurements indicate that this drag reduction rather originates from a weakening of the turbulence intensity in line with the two-dimensionalization of the large-scale flow.Comment: To appear in Journal of Fluid Mechanics Rapid

La discrétisation temporelle. Une méthode de structuration des données pour la cartographie dynamique

National audienceLa cartographie dynamique tient rarement compte du rythme des phénomènes représentés. Dès lors, les séquences composant certaines animations peuvent paraître tantôt trop rapides - avec un risque de mauvaise perception du phénomène représenté - tantôt trop lentes - avec un risque de lassitude et de perte d'attention de la part du lecteur. Aussi, cette communication propose-t-elle une méthode de structuration des données temporelles visant à préparer la construction de cartes dynamiques adaptées

Molecular Dynamics Studies of Concentrated Binary Solutions of Lanthanide Salts: Structural and Exchange Dynamics

International audienceConcentrated binary aqueous solutions of lanthanide (Nd3+ and Dy3+) salts (ClO4−, Cl−, and NO3−) have been studied by means of classical molecular dynamics (MD) simulations with explicit polarization and UV−visible spectroscopy. Pair interaction potentials, used for the MD simulations, have been developed in order to reproduce experimental hydration properties. Nd3+ and Dy3+ have been chosen because of their position in the lanthanide series: Nd3+ being a light lanthanide and Dy3+ a heavy one. They are respectively coordinated to nine and eight water molecules, in pure water, involving changes in their salt hydration structures. Both MD simulations and UV−visible experiments highlight the stronger affinity of nitrate anions toward Ln3+ compared to perchlorates and chlorides. Dissociation/association processes of Nd3+−Cl− and Nd3+−NO3− ion pairs in aqueous solution have been analyzed using potential of mean force profile calculations. Furthermore, from MD simulations, it appears that the affinity of anions (perchlorate, chloride, and nitrate) is stronger for Nd3+ than Dy3+

Direct measurements of anisotropic energy transfers in a rotating turbulence experiment

We investigate experimentally the influence of a background rotation on the energy transfers in decaying grid turbulence. The anisotropic energy flux density, ${\bf F} ({\bf r}) =$, where $\delta {\bf u}$ is the vector velocity increment over separation ${\bf r}$, is determined for the first time using Particle Image Velocimetry. We show that rotation induces an anisotropy of the energy flux $\nabla \cdot {\bf F}$, which leads to an anisotropy growth of the energy distribution $E({\bf r}) = < (\delta {\bf u})^2 >$, in agreement with the K\'arm\'an-Howarth-Monin equation. Surprisingly, our results prove that this anisotropy growth is essentially driven by a nearly radial, but orientation-dependent, energy flux density ${\bf F} ({\bf r})$.Comment: to appear in Physical Review Letters (July 8, 2011 issue

Viscous spreading of an inertial wave beam in a rotating fluid

We report experimental measurements of inertial waves generated by an oscillating cylinder in a rotating fluid. The two-dimensional wave takes place in a stationary cross-shaped wavepacket. Velocity and vorticity fields in a vertical plane normal to the wavemaker are measured by a corotating Particule Image Velocimetry system. The viscous spreading of the wave beam and the associated decay of the velocity and vorticity envelopes are characterized. They are found in good agreement with the similarity solution of a linear viscous theory, derived under a quasi-parallel assumption similar to the classical analysis of Thomas and Stevenson [J. Fluid Mech. 54 (3), 495-506 (1972)] for internal waves

Earth rotation prevents exact solid-body rotation of fluids in the laboratory

International audience–We report direct evidence of a secondary flow excited by the Earth rotation in a water-filled spherical container spinning at constant rotation rate. This so-called tilt-over flow essentially consists in a rotation around an axis which is slightly tilted with respect to the rotation axis of the sphere. In the astrophysical context, it corresponds to the flow in the liquid cores of planets forced by precession of the planet rotation axis, and it has been proposed to contribute to the generation of planetary magnetic fields. We detect this weak secondary flow using a particle image velocimetry system mounted in the rotating frame. This secondary flow consists in a weak rotation, thousand times smaller than the sphere rotation, around a horizontal axis which is stationary in the laboratory frame. Its amplitude and orientation are in quantitative agreement with the theory of the tilt-over flow excited by precession. These results show that setting a fluid in a perfect solid body rotation in a laboratory experiment is impossible — unless tilting the rotation axis of the experiment parallel to the Earth rotation axis. Introduction. – There are few examples of fluid mechanics experiments at the laboratory scale in which the Earth's Coriolis force has a measurable influence. Such experiments may be considered as fluid analogues to the Foucault pendulum. The most popular instance is certainly the drain of a bathtube vortex [1]. Although this is the subject of common misconception, it is actually possible to detect the influence of the Earth's rotation on the vortex, but only under extremely careful experimental conditions, far from the everyday experience [2]. Thermal convection is another example, in which a slow drift of the large-scale flow due to the Earth rotation has been detected in very controlled systems [3, 4]. In this letter we describe an experiment which may be considered as the most simple fluid Foucault pendulum: it consists in a volume of water enclosed in a spherical container spinning at constant rotation rate Ω 0 (fig. 1). After a transient known as spin-up, the water is expected to rotate as a solid body at the same rate Ω 0 [5]. The (a