The relative dispersion of pairs of inertial particles in incompressible, homogeneous, and isotropic turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ∼200 and 400. The evolution of both heavy and light particle pairs is analysed at varying the particle Stokes number and the fluid-to-particle density ratio. For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle velocity statistics, and it lasts until heavy particle velocities have relaxed towards the underlying flow velocities. At such large scales, a second regime starts where heavy particles separate as tracers particles would do. As a consequence, at increasing inertia, a larger transient stage is observed, and the Richardson diffusion of simple tracers is recovered only at large times and large scales. These features also arise from a statistical closure of the equation of motion for heavy particle separation that is proposed, and which is supported by the numerical results. In the case of light particles with high density ratios, strong small-scale clustering leads to a considerable fraction of pairs that do not separate at all, although the mean separation increases with time. This effect strongly alters the shape of the probability density function of light particle separations

We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible FourierNavier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-Bénard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh-Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At ∼ 0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in presence of high stratification and we quantify the asymmetric growth rate for spikes and bubbles for two dimensional RayleighTaylor systems with resolution up to Lx × Lz = 1664 × 4400 and with Rayleigh numbers up to Ra ∼ 2 × 10 10 .

International audienceIn order to understand the flow profiles of complex fluids, a crucial issue concerns the emergence of spatial correlations among plastic rearrangements exhibiting cooperativity flow behaviour at the macroscopic level. In this paper, the rate of plastic events in a Poiseuille flow is experimen-tally measured on a confined foam in a Hele-Shaw geometry. The correlation with independently measured velocity profiles is quantified by looking at the relationship between the localisation length of the velocity profiles and the localisation length of the spatial distribution of plastic events. To complement the cooperativity mechanisms studied in foam with those of other soft-glassy systems, we compare the experiments with simulations of dense emulsions based on the lattice Boltzmann method, which are performed both with, and without, wall friction. Finally, unprecedented results on the distribution of the orientation of plastic events show that there is a non-trivial correlation with the underlying local shear strain. These features, not previously re-ported for a confined foam, lend further support to the idea that cooperativity mechanisms, orig-inally invoked for concentrated emulsions (Goyon et al. 2008), have parallels in the behaviour of other soft-glassy materials

We present the results of a high resolution numerical study of two-dimensional ͑2D͒ RayleighTaylor turbulence using a recently proposed thermal lattice Boltzmann method. The goal of our study is both methodological and physical. We assess merits and limitations concerning small-and large-scale resolution/accuracy of the adopted integration scheme. We discuss quantitatively the requirements needed to keep the method stable and precise enough to simulate stratified and unstratified flows driven by thermal active fluctuations at high Rayleigh and high Reynolds numbers. We present data with spatial resolution up to 4096ϫ 10 000 grid points and Rayleigh number up to Raϳ 10 11 . The statistical quality of the data allows us to investigate velocity and temperature fluctuations, scale-by-scale, over roughly four decades. We present a detailed quantitative analysis of scaling laws in the viscous, inertial, and integral range, supporting the existence of a Bolgiano-like inertial scaling, as expected in 2D systems. We also discuss the presence of small/large intermittent deviations to the scaling of velocity/temperature fluctuations and the Rayleigh dependency of gradients flatness.

We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurations, including steady shear, elongational flows, transient shear and oscillatory flows. As an upgrade of complexity, we study the model in presence of non-ideal multicomponent interfaces, where immiscibility is introduced in the LBM description using the "Shan-Chen" model. The problem of a confined viscoelastic (Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is investigated and numerical results are compared with the predictions of various theoretical models. The proposed numerical simulations explore problems where the capabilities of LBM were never quantified before.

-By means of mesoscopic numerical simulations of a model soft-glassy material, we investigate the role of boundary roughness on the flow behaviour of the material, probing the bulk/wall and global/local rheologies. We show that the roughness reduces the wall slip induced by wettability properties and acts as a source of fluidisation for the material. A direct inspection of the plastic events suggests that their rate of occurrence grows with the fluidity field, reconciling our simulations with kinetic elasto-plastic descriptions of jammed materials. Notwithstanding, we observe qualitative and quantitative differences in the scaling, depending on the distance from the rough wall and on the imposed shear. The impact of roughness on the orientational statistics is also studied.Introduction. -The general term Soft-Glassy Materials (SGM) embraces a number of complex materials of great technological and biological relevance, whose rheology lies in between solid-like and liquid-like behaviors [1]. Dense emulsions, foams and gels are instances of such systems. Due to their importance in a host of natural and industrial processes, and to the challenge represented by their modelling for non-equilibrium statistical mechanics, SGM have been the subject of many recent experimental [2,3], theoretical [4][5][6][7] and numerical works [8]. It is widely acknowledged that such materials flow as the result of a succession of plastic rearrangements, occurring when a local configuration of constituting micro-elements (i.e. droplets for emulsions, bubbles for a foam, etc) cannot sustain the accumulated stress and relaxes it in the form of long-ranged elastic waves, which induce non-locality in the rheological properties of the system. A number of theoretical frameworks have been developed recently to take into account these non-local effects [6,7,9,10]. One of them, the Kinetic Elasto-Plastic (KEP) model [7], captures the essential phenomenology in a mean-field spirit through a diffusion-relaxation equation for the fluidity field f =γ/σ

We study the statistics of curvature and torsion of Lagrangian trajectories from direct numerical simulations of homogeneous and isotropic turbulence (at Re λ ≈ 280) in order to extract informations on the geometry of small scale coherent structures in turbulent flows. We find that, as previously observed by Braun et al [14] and by Xu et al [23], the high curvature statistics is dominated by large scale flow reversals where the velocity magnitude assumes very low values. In order to focus on small-scales signatures, we introduce a cutoff on the velocity amplitude and we study the probability distribution of time-filtered curvature conditioned only on those events when the local velocity is not that small. In this way we are able to select small-scales turbulent features, connected to vortex filaments. We show that the conditional probability density of time-filtered curvature is well reproduced by a multifractal formalism. Finally, by studying the joint statistics of curvature and torsion we find further evidences that intense and persistent events are dominated by helical type trajectories.

We present a numerical study of Rayleigh-Bénard convection disturbed by a longitudinal wind. Our results show that under the action of the wind, the vertical heat flux through the cell initially decreases, due to the mechanism of plumes-sweeping, and then increases again when turbulent forced convection dominates over the buoyancy. As a result, the Nusselt number is a non-monotonic function of the shear Reynolds number. We provide a simple model that captures with good accuracy all the dynamical regimes observed. We expect that our findings can lead the way to a more fundamental understanding of the of the complex interplay between mean-wind and plumes ejection in the Rayleigh-Bénard phenomenology.