Multi-scale model of gradient evolution in turbulent flows

A multi-scale model for the evolution of the velocity gradient tensor in fully developed turbulence is proposed. The model is based on a coupling between a ``Restricted Euler'' dynamics [{\it P. Vieillefosse, Physica A, {\bf 14}, 150 (1984)}] which describes gradient self-stretching, and a deterministic cascade model which allows for energy exchange between different scales. We show that inclusion of the cascade process is sufficient to regularize the well-known finite time singularity of the Restricted Euler dynamics. At the same time, the model retains topological and geometrical features of real turbulent flows: these include the alignment between vorticity and the intermediate eigenvector of the strain-rate tensor and the typical teardrop shape of the joint probability density between the two invariants, $R-Q$, of the gradient tensor. The model also possesses skewed, non-Gaussian longitudinal gradient fluctuations and the correct scaling of energy dissipation as a function of Reynolds number. Derivative flatness coefficients are in good agreement with experimental data.Comment: 4 pages, 4 figure

An accurate and efficient Lagrangian sub-grid model

A computationally efficient model is introduced to account for the sub-grid scale velocities of tracer particles dispersed in statistically homogeneous and isotropic turbulent flows. The model embeds the multi-scale nature of turbulent temporal and spatial correlations, that are essential to reproduce multi-particle dispersion. It is capable to describe the Lagrangian diffusion and dispersion of temporally and spatially correlated clouds of particles. Although the model neglects intermittent corrections, we show that pair and tetrad dispersion results nicely compare with Direct Numerical Simulations of statistically isotropic and homogeneous $3D$ turbulence. This is in agreement with recent observations that deviations from self-similar pair dispersion statistics are rare events

Droplet size distribution in homogeneous isotropic 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

On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by `Statistically Preserved Structures' which are associated with exact conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations.Comment: revised version with new data on Navier-Stokes eq

Velocity gradients 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 particluar 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~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 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.Comment: 7 pages, 7 figures; Physical Review E (accepted Dec 7, 2009

Intermittency and Universality in Fully-Developed Inviscid and Weakly-Compressible Turbulent Flows

We performed high resolution numerical simulations of homogenous and isotropic compressible turbulence, with an average 3D Mach number close to 0.3. We study the statistical properties of intermittency for velocity, density and entropy. For the velocity field, which is the primary quantity that can be compared to the isotropic incompressible case, we find no statistical differences in its behavior in the inertial range due either to the slight compressibility or to the different dissipative mechanism. For the density field, we find evidence of ``front-like'' structures, although no shocks are produced by the simulation.Comment: Submitted to Phys. Rev. Let

Inverse energy cascade in three-dimensional isotropic turbulence

In turbulent flows kinetic energy is spread by nonlinear interactions over a broad range of scales. Energy transfer may proceed either toward small scales or in the reverse direction. The latter case is peculiar of two-dimensional (2D) flows. Interestingly, a reversal of the energy flux is observed also in three-dimensional (3D) geophysical flows under rotation and/or confined in thin layers. The question is whether this phenomenon is enforced solely by external anisotropic mechanisms or it is intimately embedded in the Navier-Stokes (NS) equations. Here we show that an inverse energy cascade occurs also in 3D isotropic flow. The flow is obtained from a suitable surgery of the NS equations, keeping only triadic interactions between sign-defined helical modes, preserving homogeneity and isotropy and breaking reflection invariance. Our findings highlight the role played by helicity in the energy transfer process and show that both 2D and 3D properties naturally coexist in all flows in nature.Comment: 4 pages, 4 figure

Population dynamics at high Reynolds number

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.Comment: 5 pages, 5 figure

Effects of forcing in three dimensional turbulent flows

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power law spectrum, $E_f(k)\sim k^{3-y}$. Numerical simulations are performed at different resolutions up to $512^3$. We show that at varying the spectrum slope $y$, small-scale turbulent fluctuations change from a {\it forcing independent} to a {\it forcing dominated} statistics. We argue that the critical value separating the two behaviours, in three dimensions, is $y_c=4$. When the statistics is forcing dominated, for $y<y_c$, we find dimensional scaling, i.e. intermittency is vanishingly small. On the other hand, for $y>y_c$, we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of {\it universality} in turbulent flows.Comment: 4 pages, 4 figure

Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows

Breakup of small aggregates in fully developed turbulence is studied by means of direct numerical simulations in a series of typical bounded and unbounded flow configurations, such as a turbulent channel flow, a developing boundary layer and homogeneous isotropic turbulence. The simplest criterion for breakup is adopted, whereas aggregate breakup occurs when the local hydrodynamic stress $\sigma\sim \varepsilon^{1/2}$, with $\varepsilon$ being the energy dissipation at the position of the aggregate, overcomes a given threshold $\sigma_\mathrm{cr}$, which is characteristic for a given type of aggregates. Results show that the breakup rate decreases with increasing threshold. For small thresholds, it develops a universal scaling among the different flows. For high thresholds, the breakup rates show strong differences between the different flow configurations, highlighting the importance of non-universal mean-flow properties. To further assess the effects of flow inhomogeneity and turbulent fluctuations, theresults are compared with those obtained in a smooth stochastic flow. Furthermore, we discuss the limitations and applicability of a set of independent proxies.Comment: 15 pages, 12 figures, Refinded discussion in Section 2.1, results unchange