We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024 3 collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr M over a large range, namely, 0.01 ≤ Pr M ≤ 10. We obtain data for a wide variety of statistical measures such as probability distribution functions (PDFs) of moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterise intermittency, isosurfaces of quantities such as the moduli of the vorticity and current, and joint PDFs such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from larger intermittency in the magnetic field than in the velocity field, at large Pr M , to smaller intermittency in the magnetic field than in the velocity field, at low Pr M . Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr M , multiscaling exponent ratios agree, at least within our errorbars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

We study the physics of droplet breakup in a statistically stationary homogeneous and isotropic turbulent flow by means of high resolution numerical investigations based on the multicomponent lattice Boltzmann method. We verified the validity of the criterion proposed by Hinze (1955) for droplet breakup and we measured the full probability distribution function (pdf) of droplets radii at different Reynolds numbers and for different volume fraction. By means of a Lagrangian tracking we could follow individual droplets along their trajectories, define a local Weber number based on the velocity gradients and study its cross-correlation with droplet deformation.Comment: 10 pages, 6 figure

We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments.

The existence of drag reduction by polymer additives, well established for wall-bounded turbulent flows, is controversial in homogeneous, isotropic turbulence. To settle this controversy we carry out a high-resolution direct numerical simulation (DNS) of decaying, homogeneous, isotropic turbulence with polymer additives. Our study reveals clear manifestations of drag-reduction-type phenomena: On the addition of polymers to the turbulent fluid we obtain a reduction in the energy dissipation rate, a significant modification of the fluid energy spectrum especially in the deep-dissipation range, a suppression of small-scale intermittency, and a decrease in small-scale vorticity filaments.

International audienceBy using direct numerical simulations at unprecedented resolution we study turbulence under rotation in presence of simultaneous direct andinverse cascades. The accumulation of energy at large scale leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By seeding the flow with millions of inertial particles we quantify -for the first time- the effects of those coherent vertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitatively show that extreme fluctuations, leading to deviations from anormal-distributed statistics, result from the entangled interaction of the vertical structures with the turbulent background. Finally, we present the first --ever-- measurement of the relative importance between Stokes drag, Coriolis and centripetal forces along the trajectories of inertial particles. We discovered that vortical coherent structures lead to unexpected diffusion properties for heavy and light particles in the directions parallel and perpendicular to the rotation axis

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Abstract. We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.

We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field. We show that the interplay between turbulent dynamics and population growth and saturation leads to quasi-localization and a remarkable reduction in the carrying capacity. The statistical properties of the population density are investigated and quantified via multifractal scaling analysis. We also investigate numerically the singular limit of negligibly small growth rates and delocalization of population ridges triggered by uniform advection. where C(x, t) is a continuous variable describing the concentration of micro-organisms, D is the diffusion coefficient and µ is the growth rate. As an example of "life at high Reynolds number", we could take Eq.(1) to represent the density of the marine cyanobacterium Synechococcus [3] under conditions of abundant nutrients, so that µ ∼ constant. As discussed in [4], an advecting compressible turbulent flow leads to highly non-trivial dynamics. Although the results of [4] were obtained only in one dimension using a synthetic advecting flow from a shell model of turbulence, two striking effects were observed: the concentration field C(x, t) is strongly localized near transient but long-lived sinks of the turbulent flows for small enough growth rate µ; in the same limit, the space-time average concentration (denoted in the following as carrying capacity) becomes much smaller than its maximum value 1. Both effects are relevant in biological applications [5].In this Letter, we present new numerical results for more realistic two dimensional turbulent flows. We assume that the microorganism concentration field C(x, t), whose dynamics is described by Eq. (1), lies on a planar surface of constant height in a three dimensional fully developed turbulent flow with periodic boundary conditions. Such a system could be a rough approximation to photosynthetic microorganisms that actively control their bouyancy to manitain a fixed depth below the surface of a turbulent fluid [6]. As a consequence of this choice, the flow field in the two dimensional slice becomes compressible [7]. We consider here a turbulent advecting field u(x, t) described by the Navier-Stokes equations, and nondimensionalize time by the Kolmogorov dissipation time-scale τ η ≡ (ν/ǫ) 1/2 and space by the Kolmogorov length-scale η ≡ (ν 3 /ǫ) 1/4 , where ǫ is the mean rate of energy dissipation and ν is the kinematic viscosity. The non-dimensional numbers charecterizing the evolution of the scalar field C(x, t) are then the Schmidt number Sc = ν/D and the non-dimensional time µτ η . A particularly interesting regime arises when the doubling time τ g ≡ µ −1 is somewhere in the middle of the inertial range of eddy turnover times (τ r = r/δ r u, where δ r u is the typical velocity difference across length scale r) that characterize the turbulence. Although the underlying turbulent energy cascade is somewhat different [8], this situation arises for oceanic cyanobacteria and phytoplankton, ...