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

Cascades d’énergie et turbulence d’ondes dans une expérience de turbulence en rotation

We present an experimental study of the effect of global rotation on statistically stationary turbulent flows. In a first experiment, the flow is generated with counter-rotating vortex generators acting in a periodic motion in a rotating tank filled with water. Resolved in time measurements of the three component of the velocity are performed, in both horizontal and vertical planes, thanks to a stereoscopic particle image velocimetry system embarked in the rotating frame. The flow has, in accordance with the bibliography, a strong anisotropy and shows the emergence of an energetic 2D flow. For the first time experimentally, we describe the global scale by scale energy budget of a rotating turbulence through the measure of the terms of the inhomogeneous generalization of Kármán-Howarth-Monin equation. We thus reveal a double energy cascade: direct at small scale and inverse at large scale, the scale of cascade reversal decreasing with the rotation rate. Then, we evaluate the injected power into the system which is intrinsically linked to the inhomogeneities of the flow. The energy input comes from auto-advection of turbulent structures through the boundaries of the area considered. It is broadband in scales and spreads as ration increases. We then focus on relevance of inertial wave turbulence models. We first perform a spatiotemporal analysis which reveals the presence of linear inertial waves at large frequencies and scales. However, we show that the spatiotemporal signature of small frequencies and scales are scrambled by the linear process of stochastic sweeping by the 2D energetic mode. In a second experiment, the flow is created thanks to a four-rectangular-blade impeller in a closed rotating tank. We estimate the energy dissipation rate through the measure of the injected power by the motor that drives the impeller. We then bring, for the first time, a direct evidence of the scaling law predicted by inertial wave turbulence models which is fallen by a factor Rossby compared to the scaling law of 3D homogeneous isotropic turbulence.Nous présentons une étude expérimentale de l’effet d’une rotation d’ensemble sur les écoulements turbulents statistiquement stationnaires. Dans une première expérience, l’écoulement est entretenu à l’aide de générateurs de tourbillons contrarotatifs agissant de manière périodique dans une cuve en rotation remplie d’eau. Des mesures résolues en temps des trois composantes de la vitesse sont réalisées, dans des plans horizontaux et verticaux, à l’aide d’un dispositif de vélocimétrie stéréoscopique par images de particules embarqué dans le référentiel tournant. L’écoulement étudié présente, conformément à la littérature, une forte anisotropie et montre l’émergence d’un mode 2D énergétique. Pour la première fois expérimentalement, nous décrivons le bilan global d’énergie entre échelles d’une turbulence en rotation à travers la mesure des termes de l’équation de Kármán-Howarth-Monin généralisée au cas inhomogène. Nous mettons ainsi en évidence la présence d’une double cascade d’énergie : directe à petite échelle et inverse à grande échelle, l’échelle de renversement des cascades étant décroissante avec le taux de rotation. Nous évaluons ensuite la puissance injectée qui est intrinsèquement liée au caractère inhomogène de l’écoulement. L’injection d’énergie provient de l’auto-advection des structures turbulentes traversant les frontières de la zone de contrôle. Elle est large bande en échelles et s’étale à mesure que la rotation croît. Nous nous intéressons ensuite à la pertinence des modèles de turbulence d’ondes d’inertie. Nous réalisons tout d’abord une analyse spatio-temporelle qui révèle la présence d’ondes d’inertie linéaires à grande échelle spatiale et grande fréquence temporelle. En revanche, nous montrons que la signature spatio-temporelle des structures turbulentes associées aux échelles et fréquences faibles est brouillée par le processus linéaire de balayage stochastique par le mode 2D énergétique. Dans une seconde expérience, l’écoulement est engendré par une hélice constituée de quatre pales rectangulaires dans une cuve fermée en rotation. Nous évaluons le taux de dissipation d’énergie à travers la mesure de la puissance injectée par le moteur qui entraîne l’hélice. Nous fournissons alors, pour la première fois, une preuve directe de la loi d’échelle du taux de dissipation d’énergie prédite par la turbulence d’onde d’inertie qui est diminuée d’un facteur Rossby par rapport à la loi d’échelle de la turbulence 3D homogène et isotrope

FluidImage, a libre framework for scientific treatments of large sets of images

National audienceFluidImage A software for the fluid dynamic community, by the fluid dynamic communityA libre framework for scientific treatments of large sets of imagesEasy, safe and efficient for all users, nice for the developer

Impact of dissipation on the energy spectrum of experimental turbulence of gravity surface waves

We discuss the impact of dissipation on the development of the energy spectrum in wave turbulence of gravity surface waves with emphasis on the effect of surface contamination. We performed experiments in the Coriolis facility which is a 13-m diameter wave tank. We took care of cleaning surface contamination as well as possible considering that the surface of water exceeds 100~m$^2$. We observe that for the cleanest condition the frequency energy spectrum shows a power law decay extending up to the gravity capillary crossover (14 Hz) with a spectral exponent that is increasing with the forcing strength and decaying with surface contamination. Although slightly higher than reported previously in the literature, the exponent for the cleanest water remains significantly below the prediction from the Weak Turbulence Theory. By discussing length and time scales, we show that weak turbulence cannot be expected at frequencies above 3 Hz. We observe with a stereoscopic reconstruction technique that the increase with the forcing strength of energy spectrum beyond 3~Hz is mostly due to the formation and strenghtening of bound waves.Comment: accepted for publication in Physical Review Fluid

Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility

We investigate experimentally stratified turbulence forced by waves. Stratified turbulence is present in oceans and it is expected to be dominated by nonlinear interaction of internal gravity waves as described by the Garrett & Munk spectrum. In order to reach turbulent regimes dominated by stratification we use the Coriolis facility in Grenoble (France) which large size enables us to reach regimes with both low Froude number and large Reynolds number. Stratification is obtained by using vertically linearly varying salt concentration and we force large scale waves in a $6\times6\times 1$ m$^3$ domain. We perform time-resolved PIV to probe the space-time structure of the velocity field. We observe a wide band spectrum which is made of waves. Discrete modes are observed due to the square shape of the flow container as well as a continuum part which appears consistent with an axisymmetric superposition of random weakly nonlinear waves. Our observations support the interpretation of turbulence of a strongly stratified fluid as wave turbulence of internal waves although our spectrum is quite different from the Garrett & Munk spectrum. Weak turbulence proceeds down to a small cutoff length scale (the buoyancy wavelength) at which a transition to more strongly nonlinear turbulence is expected.Comment: accepted for publication in Physical Review Fluid

Гранитоиды обрамления Криворожской структуры. Проблемы корреляции геологических тел и комплексов

Current population genetic models fail to cope with genetic differentiation for species with large, contiguous and heterogeneous distribution. We show that in such a case, genetic differentiation can be predicted at equilibrium by circuit theory, where conductance corresponds to abundance in species distribution models (SDM). Circuit-SDM approach was used for the phylogeographic study of the lepidopteran cereal stemborer Busseola fusca Füller (Noctuidae) across sub-Saharan Africa. Species abundance was surveyed across its distribution range. SDM models were optimized and selected by cross validation. Relationship between observed matrices of genetic differentiation between individuals, and matrices of resistance distance was assessed through Mantel tests and redundancy discriminant analyses (RDA). A total of 628 individuals from 130 localities in 17 countries were genotyped at 7 microsatellite loci. Six population clusters were found based on a Bayesian analysis. The eastern margin of Dahomey Gap between East and West Africa was the main factor of genetic differentiation. The SDM projections at present, last interglacial and last glacial maximum periods were used for estimation of circuit resistance between locations of genotyped individuals. For all periods of time, when using either all individuals or only East-African individuals, partial Mantel r and RDA analyses conditioning on geographic distance were found significant. Under future projections (year 2080), partial r and RDA significance were different. From this study, it is concluded that analytical solutions provided by circuit theory are useful for the evolutionary management of populations and for phylogeographic analysis when coalescence times are not accessible by approximate Bayesian simulations

RNA recognition by Npl3p reveals U2 snRNA-binding compatible with a chaperone role during splicing

The conserved SR-like protein Npl3 promotes splicing of diverse pre-mRNAs. However, the RNA sequence(s) recognized by the RNA Recognition Motifs (RRM1 & RRM2) of Npl3 during the splicing reaction remain elusive. Here, we developed a split-iCRAC approach in yeast to uncover the consensus sequence bound to each RRM. High-resolution NMR structures show that RRM2 recognizes a 5´-GNGG-3´ motif leading to an unusual mille-feuille topology. These structures also reveal how RRM1 preferentially interacts with a CC-dinucleotide upstream of this motif, and how the inter-RRM linker and the region C-terminal to RRM2 contribute to cooperative RNA-binding. Structure-guided functional studies show that Npl3 genetically interacts with U2 snRNP specific factors and we provide evidence that Npl3 melts U2 snRNA stem-loop I, a prerequisite for U2/U6 duplex formation within the catalytic center of the B$^{act}$ spliceosomal complex. Thus, our findings suggest an unanticipated RNA chaperoning role for Npl3 during spliceosome active site formation