arXiv subjects

Luca Biferale

Publications and source records attributed to Luca Biferale.

142 records · Page 8Linked to original sources

arXiv2009

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.

physics.flu-dyn↗

arXiv2009

Statistics of small scale vortex filaments in turbulence

We study the statistical properties of coherent, small-scales, filamentary-like structures in Turbulence. In order to follow in time such complex spatial structures, we integrate Lagrangian and Eulerian measurements by seeding the flow with light particles. We show that light particles preferentially concentrate in small filamentary regions of high persistent vorticity (vortex filaments). We measure the fractal dimension of the attracting set and the probability that two particles do not separate for long time lapses. We fortify the signal-to-noise ratio by exploiting multi-particles correlations on the dynamics of bunches of particles. In doing that, we are able to give a first quantitative estimation of the vortex-filaments life-times, showing the presence of events as long as the integral correlation time. The same technique introduced here could be used in experiments as long as one is capable to track clouds of bubbles in turbulence for a relatively long period of time, at high Reynolds numbers; shading light on the dynamics of small-scale vorticity in realistic turbulent flows.

physics.flu-dyn↗

arXiv2007

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.

nlin.CD↗

arXiv2006

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.

nlin.CD↗

arXiv2006

Lyapunov exponents of heavy particles in turbulence

Lyapunov exponents of heavy particles and tracers advected by homogeneous and isotropic turbulent flows are investigated by means of direct numerical simulations. For large values of the Stokes number, the main effect of inertia is to reduce the chaoticity with respect to fluid tracers. Conversely, for small inertia, a counter-intuitive increase of the first Lyapunov exponent is observed. The flow intermittency is found to induce a Reynolds number dependency for the statistics of the finite time Lyapunov exponents of tracers. Such intermittency effects are found to persist at increasing inertia.

nlin.CD↗

arXiv2006

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.

nlin.CD↗

arXiv2006

On the effects of vortex trapping on the velocity statistics of tracers and heavy particle in turbulent flows

The Lagrangian statistics of heavy particles and of fluid tracers transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. The Lagrangian velocity structure functions are measured in a time range spanning about three decades, from a tenth of the Kolmogorov timescale up to a few large-scale eddy turnover time. Strong evidence is obtained that fluid tracers statistics are contaminated in the time span 1-10 times the dissipative time scale by a bottleneck effect due to vortex trapping. This effect is found to be significantly reduced for heavy particles which are expelled from vortices by inertia. These findings help in clarifying the results of a recent study by H. Xu et al. Phys. Rev. Lett. 96, 024503 (2006), where differences between experimental and numerical results on scaling properties of fluid tracers were reported.

nlin.CD↗

arXiv2005

Joint statistics of acceleration and vorticity in fully developed turbulence

We report results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We present results concerning acceleration statistics and the statistics of trapping by vortex filaments conditioned to the local values of vorticity and enstrophy. We distinguish two different behaviors between the joint statistics of vorticity and centripetal acceleration or vorticity and longitudinal acceleration.

nlin.CD↗

arXiv2004

Anisotropy in Turbulent Flows and in Turbulent Transport

We discuss the problem of anisotropy and intermittency in statistical theory of high Reynolds-number turbulence (and turbulent transport). We present a detailed description of the new tools that allow effective data analysis and systematic theoretical studies such as to separate isotropic from anisotropic aspects of turbulent statistical fluctuations. Employing the invariance of the equations of fluid mechanics to all rotations, we show how to decompose the (tensorial) statistical objects in terms of the irreducible representation of the SO(3) symmetry group. For the case of turbulent advection of passive scalar or vector fields, this decomposition allows rigorous statements to be made: (i) the scaling exponents are universal, (ii) the isotropic scaling exponents are always leading, (iii) the anisotropic scaling exponents form a discrete spectrum which is strictly increasing as a function of the anisotropic degree. Next we explain how to apply the SO(3) decomposition to the statistical Navier-Stokes theory. We show how to extract information about the scaling behavior in the isotropic sector. Doing so furnishes a systematic way to assess the universality of the scaling exponents in this sector, clarifying the anisotropic origin of the many measurements that claimed the opposite. A systematic analysis of Direct Numerical Simulations and of experiments provides a strong support to the proposition that also for the non-linear problem there exists foliation of the statistical theory into sectors of the symmetry group. The exponents appear universal in each sector, and again strictly increasing as a function of the anisotropic degreee.

nlin.CD↗

arXiv2004

Anisotropic fluctuations in turbulent sheared flows

An experimental analysis of small-scales anisotropic turbulent fluctuations has been performed in two different flows. We analyzed anisotropic properties of an homogeneous shear flows and of a turbulent boundary layer by means of two cross-wire probes to obtain multi-point multi-component measurements. Data are analyzed at changing inter-probe separation without the use of Taylor hypothesis. The results are consistent with the ``exponent-only'' scenario for universality, i.e. all experimental data can be fit by fixing the same set of anisotropic scaling exponents at changing only prefactors, for different shear intensities and boundary conditions.

nlin.CD↗

arXiv2003

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 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.

nlin.CD↗

arXiv2003

Intermittency in Turbulence: computing the scaling exponents in shell models

We discuss a stochastic closure for the equation of motion satisfied by multi-scale correlation functions in the framework of shell models of turbulence. We give a systematic procedure to calculate the anomalous scaling exponents of structure functions by using the exact constraints imposed by the equation of motion. We present an explicit calculation for fifth order scaling exponent at varying the free parameter entering in the non-linear term of the model. The same method applied to the case of shell models for Kraichnan passive scalar provides a connection between the concept of zero-modes and time-dependent cascade processes.

nlin.CD↗

arXiv2002

A Gibbs-like measure for single-time, multi-scale energy transfer in stochastic signals and Shell Model of turbulence

A Gibbs-like approach for simultaneous multi-scale correlation functions in random, time-dependent, multiplicative processes for the turbulent energy cascade is investigated. We study the optimal log-normal Gibbs-like distribution able to describe the subtle effects induced by non-trivial time dependency on both single-scale (structure functions) and multi-scale correlation functions. We provide analytical expression for the general multi-scale correlation functions in terms of the two-point correlations between multipliers and we show that the log-normal distribution is already accurate enough to reproduce quantitatively many of the observed behavior. The main result is that non-trivial time effects renormalize the Gibbs-like effective potential necessary to describe single-time statistics. We also present a generalization of this approach to more general, non log-normal, potential. In the latter case one obtains a formal expansion of both structure functions and multi-scale correlations in terms of cumulants of all orders.

nlin.CD↗

arXiv2002

Intermittency in Turbulence: Multiplicative random process in space and time

We present a simple stochastic algorithm for generating multiplicative processes with multiscaling both in space and in time. With this algorithm we are able to reproduce a synthetic signal with the same space and time correlation as the one coming from shell models for turbulence and the one coming from a turbulent velocity field in a quasi-Lagrangian reference frame.

nlin.CD↗

arXiv2000

Anisotropic Homogeneous Turbulence: hierarchy and intermittency of scaling exponents in the anisotropic sectors

We present the first measurements of anisotropic statistical fluctuations in perfectly homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors and hierarchical ordering of anisotropies on a direct numerical simulation of a three dimensional random Kolmogorov flow. We achieved an homogeneous and anisotropic statistical ensemble by randomly shifting the forcing phases. We observe high intermittency as a function of the order of the velocity correlation within each fixed anisotropic sector and a hierarchical organization of scaling exponents at fixed order of the velocity correlation at changing the anisotropic sector.

nlin.CD↗

arXiv2000

Probing structures in channel flow through SO(3) and SO(2) decomposition

SO(3) and SO(2) decompositions of numerical channel flow turbulence are performed. The decompositions are used to probe, characterize, and quantify anisotropic structures in the flow. Close to the wall the anisotropic modes are dominant and reveal the flow structures. The SO(3) decomposition does not converge for large scales as expected. However, in the shear buffer layer it also does not converge for small scales, reflecting the lack of small scales isotropization in that part of the channel flow.

nlin.CD↗