Dispersion of Molecular Patterns Written in Turbulent Air.

We study the dispersion of tiny molecular clouds in turbulence by writing patterns in turbulent air and following their deformation in time. The writing is done by fusing O_{2} and N_{2} molecules into NO in the focus of a strong ultraviolet laser beam. By crossing several of these laser beams, patterns that have both small and large scales can be painted. The patterns are visualized a while later by inducing fluorescence of the NO molecules with a second UV laser and registering the image. The width of the lines that make the pattern is approximately 50 µm, a few times the Kolmogorov length η, the smallest length scale in turbulence, while the overall size of the patterns (≈4 mm) is inside the inertial range of the used turbulent jet flow. At small scales molecular clouds disperse under the joint action of molecular diffusion and turbulence. The experiments reveal for the first time this subtle, yet very important interaction. At macroscales (≈200 η) we verify the Batchelor dispersion of objects whose size is inside the inertial range; however, the expected influence of molecular diffusion is smaller than the accuracy of the experiments.

Statistical properties of two-dimensional elastic turbulence.

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylor's hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static pointlike numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylor's frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly nonhomogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.

How the growth of ice depends on the fluid dynamics underneath.

Convective flows coupled with solidification or melting in water bodies play a major role in shaping geophysical landscapes. Particularly in relation to the global climate warming scenario, it is essential to be able to accurately quantify how water-body environments dynamically interplay with ice formation or melting process. Previous studies have revealed the complex nature of the icing process, but have often ignored one of the most remarkable particularities of water, its density anomaly, and the induced stratification layers interacting and coupling in a complex way in the presence of turbulence. By combining experiments, numerical simulations, and theoretical modeling, we investigate solidification of freshwater, properly considering phase transition, water density anomaly, and real physical properties of ice and water phases, which we show to be essential for correctly predicting the different qualitative and quantitative behaviors. We identify, with increasing thermal driving, four distinct flow-dynamics regimes, where different levels of coupling among ice front and stably and unstably stratified water layers occur. Despite the complex interaction between the ice front and fluid motions, remarkably, the average ice thickness and growth rate can be well captured with the theoretical model. It is revealed that the thermal driving has major effects on the temporal evolution of the global icing process, which can vary from a few days to a few hours in the current parameter regime. Our model can be applied to general situations where the icing dynamics occur under different thermal and geometrical conditions.

Effects of large-scale advection and small-scale turbulent diffusion on vertical phytoplankton dynamics.

Turbulence has been recognized as a factor of paramount importance for the survival or extinction of sinking phytoplankton species. However, dealing with its multiscale nature in models of coupled fluid and biological dynamics is a formidable challenge. Advection by coherent structures, such as those related to winter convection and Langmuir circulation, is also recognized to play a role in the survival and localization of phytoplankton. In this work we revisit a theoretically appealing model for phytoplankton vertical dynamics, and numerically investigate how large-scale fluid motions affect the survival conditions and the spatial distribution of the biological population. For this purpose, and to work with realistic parameter values, we adopt a kinematic flow field to account for the different spatial and temporal scales of turbulent motions. The dynamics of the population density are described by an advection-reaction-diffusion model with a spatially heterogeneous growth term proportional to sunlight availability. We explore the role of fluid transport by progressively increasing the complexity of the flow in terms of spatial and temporal scales. We find that, due to the large-scale circulation, phytoplankton accumulates in downwelling regions and its growth is reduced, confirming previous indications in slightly different conditions. We then explain the observed phenomenology in terms of a plankton filament model. Moreover, by contrasting the results in our different flow cases, we show that the large-scale coherent structures have an overwhelming importance. Indeed, we find that smaller-scale motions only quite weakly affect the dynamics, without altering the general mechanism identified. Such results are relevant for parametrizations in numerical models of phytoplankton life cycles in realistic oceanic flow conditions.

Robustness of heat transfer in confined inclined convection at high Prandtl number.

We investigate the dependency of the magnitude of heat transfer in a convection cell as a function of its inclination by means of experiments and simulations. The study is performed with a working fluid of large Prandtl number, Pr≃480, and at Rayleigh numbers Ra≃10^{8} and Ra≃5×10^{8} in a quasi-two-dimensional rectangular cell with unit aspect ratio. By changing the inclination angle (ß) of the convection cell, the character of the flow can be changed from moderately turbulent, for ß=0^{∘}, to laminar and steady at ß=90^{∘}. The global heat transfer is found to be insensitive to the drastic reduction of turbulent intensity, with maximal relative variations of the order of 20% at Ra≃10^{8} and 10% at Ra≃5×10^{8}, while the Reynolds number, based on the global root-mean-square velocity, is strongly affected with a decay of more than 85% occurring in the laminar regime. We show that the intensity of the heat flux in the turbulent regime can be only weakly enhanced by establishing a large-scale circulation flow by means of small inclinations. However, in the laminar regime the heat is transported solely by a slow large-scale circulation flow which exhibits large correlations between the velocity and temperature fields. For inclination angles close to the transition regime in-between the turbulentlike and laminar state, a quasiperiodic heat-flow bursting phenomenon is observed.

Particle-laden two-dimensional elastic turbulence.

The aggregation properties of heavy inertial particles in the elastic turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are investigated by means of extensive numerical simulations in two dimensions. Both the small- and large-scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the properties of the advecting viscoelastic flow. We find that particles preferentially accumulate on thin highly elastic propagating structures and that this effect is the largest for intermediate values of particle inertia. We provide a quantitative characterization of this phenomenon that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of correlation dimension close to 1. At larger scales, particles are found to undergo turbophoretic-like segregation. Indeed, our results indicate a close relationship between the profiles of particle density and fluid velocity fluctuations. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing.

Microbubbles and Microparticles are Not Faithful Tracers of Turbulent Acceleration.

We report on the Lagrangian statistics of acceleration of small (sub-Kolmogorov) bubbles and tracer particles with Stokes number St≪1 in turbulent flow. At a decreasing Reynolds number, the bubble accelerations show deviations from that of tracer particles; i.e., they deviate from the Heisenberg-Yaglom prediction and show a quicker decorrelation despite their small size and minute St. Using direct numerical simulations, we show that these effects arise due the drift of these particles through the turbulent flow. We theoretically predict this gravity-driven effect for developed isotropic turbulence, with the ratio of Stokes to Froude number or equivalently the particle drift velocity governing the enhancement of acceleration variance and the reductions in correlation time and intermittency. Our predictions are in good agreement with experimental and numerical results. The present findings are relevant to a range of scenarios encompassing tiny bubbles and droplets that drift through the turbulent oceans and the atmosphere. They also question the common usage of microbubbles and microdroplets as tracers in turbulence research.

Finite-volume versus streaming-based lattice Boltzmann algorithm for fluid-dynamics simulations: A one-to-one accuracy and performance study.

A finite-volume (FV) discretization method for the lattice Boltzmann (LB) equation, which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the successful simulation of high-Rayleigh number convective flow performed by a lattice Boltzmann FV-based algorithm with wall grid refinement.

Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].

Rotation rate of rods in turbulent fluid flow.

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape.

Exploring the limits of granular hydrodynamics: a horizontal array of inelastic particles.

The limits of granular hydrodynamics are explored in the context of the one-dimensional granular system introduced by Du, Li, and Kadanoff [Phys. Rev. Lett. 74, 1268 (1995)]. The density profile of the characteristic steady state, in which a single particle commutes between the driving wall and a dense cluster, is well captured by a hydrodynamic description provided that the finite size of the particles is incorporated. The temperature, however, is not well described: since all energy exchange is located at the border of the cluster, it is precisely for this quantity that the continuum approach breaks down.

Velocity-gradient statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame.

We present an investigation of the statistics of velocity gradient related quantities, in particular energy dissipation rate and enstrophy, along the trajectories of fluid tracers and of heavy/light particles advected by a homogeneous and isotropic turbulent flow. The refined similarity hypothesis (RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the Lagrangian context and then tested along the particle trajectories. The study is performed on state-of-the-art numerical data resulting from numerical simulations up to Re(lambda) approximately 400 with 2048(3) collocation points. When particles have small inertia, we show that the Lagrangian formulation of the RSH is well verified for time lags larger than the typical response time tau(p) of the particle. In contrast, in the large inertia limit when the particle response time approaches the integral time scale of the flow, particles behave nearly ballistic, and the Eulerian formulation of RSH holds in the inertial range.

Quantifying turbulence-induced segregation of inertial particles.

Particles with different density from the advecting turbulent fluids cluster due to the different response of light and heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation of dilute polydisperse inertial particles evolving in turbulent flow, as obtained from direct numerical simulation of homogeneous isotropic turbulence. We introduce an indicator of segregation amongst particles of different inertia and/or size, from which a length scale r_{seg}, quantifying the segregation degree between two particle types, is deduced.

Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point.

As shown in earlier work [Ahlers, J. Fluid Mech. 569, 409 (2006)], non-Oberbeck-Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Bénard convection in water and also in glycerol are governed by the temperature dependences of the kinematic viscosity and the thermal diffusion coefficient. If the working fluid is ethane close to the critical point, the origin of non-Oberbeck-Boussinesq corrections is very different, as will be shown in the present paper. Namely, the main origin of NOB corrections then lies in the strong temperature dependence of the isobaric thermal expansion coefficient beta(T). More precisely, it is the nonlinear T dependence of the density rho(T) in the buoyancy force that causes another type of NOB effect. We demonstrate this through a combination of experimental, numerical, and theoretical work, the last in the framework of the extended Prandtl-Blasius boundary-layer theory developed by Ahlers as cited above. The theory comes to its limits if the temperature dependence of the thermal expension coefficient beta(T) is significant. The measurements reported here cover the ranges 2.1

Evidences of Bolgiano-Obhukhov scaling in three-dimensional Rayleigh-Bénard convection.

We present different results from high-resolution high-statistics direct numerical simulations of a three-dimensional convective cell. We test the fundamental physical picture of the presence of both a Bolgiano-Obhukhov-like and a Kolmogorov-like regime. We find that the dimensional predictions for these two distinct regimes (characterized, respectively, by an active and passive role of the temperature field) are consistent with our analysis.