arXiv subjects

L. Biferale

Publications and source records attributed to L. Biferale.

At least 91 records · Page 5Linked to original sources

arXiv2001

Statistical conservation laws in turbulent transport

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. We propose that with very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments (without forcing the transported fields) we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas.

nlin.CD↗

arXiv2001

Universality in passively advected hydrodynamic fields: the case of a passive vector with pressure

Universality of statistical properties of passive quantities advected by turbulent velocity fields at changing the passive forcing mechanism is discussed. In particular, we concentrate on the statistical properties of an hydrodynamic system with pressure. We present theoretical arguments and preliminary numerical results which show that the fluxes of passive vector field and of the velocity field have the same scaling behavior. By exploiting such a property, we propose a way to compute the anomalous exponents of three dimensional turbulent velocity fields. Our findings are in agreement within 5% with experimental values of the anomalous exponents.

nlin.CD↗

arXiv2000

Isotropy vs anisotropy in small-scale turbulence

The decay of large-scale anisotropies in small-scale turbulent flow is investigated. By introducing two different kinds of estimators we discuss the relation between the presence of a hierarchy for the isotropic and the anisotropic scaling exponents and the persistence of anisotropies. Direct measurements from a channel flow numerical simulation are presented.

nlin.CD↗

arXiv2000

Exit-Times and {\Large $ε$}-Entropy for Dynamical Systems, Stochastic Processes, and Turbulence

We present a comprehensive investigation of $ε$-entropy, $h(ε)$, in dynamical systems, stochastic processes and turbulence. Particular emphasis is devoted on a recently proposed approach to the calculation of the $ε$-entropy based on the exit-time statistics. The advantages of this method are demonstrated in examples of deterministic diffusive maps, intermittent maps, stochastic self-affine and multi-affine signals and experimental turbulent data. Concerning turbulence, the multifractal formalism applied to the exit time statistics allows us to predict that $h(ε)\sim ε^{-3}$ for velocity time measurement. This power law is independent of the presence of intermittency and has been confirmed by the experimental data analysis. Moreover, we show that the $ε$-entropy density of a 3-dimensional velocity field is affected by the correlations induced by the sweeping of large scales.

nlin.CD↗

arXiv2000

Statistics of pressure and of pressure-velocity correlations in isotropic turbulence

Some pressure and pressure-velocity correlation in a direct numerical simulations of a three-dimensional turbulent flow at moderate Reynolds numbers have been analyzed. We have identified a set of pressure-velocity correlations which posseses a good scaling behaviour. Such a class of pressure-velocity correlations are determined by looking at the energy-balance across any sub-volume of the flow. According to our analysis, pressure scaling is determined by the dimensional assumption that pressure behaves as a ``velocity squared'', unless finite-Reynolds effects are overwhelming. The SO(3) decompositions of pressure structure functions has also been applied in order to investigate anisotropic effects on the pressure scaling.

nlin.CD↗

arXiv1999

An exit-time approach to $ε$-entropy

An efficient approach to the calculation of the $ε$-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations are larger than a certain threshold $ε$, i.e., by looking at the exit-time statistics. The practical and theoretical advantages of our method with respect to the usual one are shown by the examples of a deterministic map and a self-affine stochastic process.

chao-dyn↗

arXiv1999

About coherent structures in random shell models for passive scalar advection

A study of anomalous scaling in models of passive scalar advection in terms of singular coherent structures is proposed. The stochastic dynamical system considered is a shell model reformulation of Kraichnan model. We extend the method introduced in \cite{DDG99} to the calculation of self-similar instantons and we show how such objects, being the most singular events, are appropriate to capture asymptotic scaling properties of the scalar field. Preliminary results concerning the statistical weight of fluctuations around these optimal configurations are also presented.

chao-dyn↗

arXiv1999

Nonperturbative Spectrum of Anomalous Scaling Exponents in the Anisotropic Sectors of Passively Advected Magnetic Fields

We address the scaling behavior of the covariance of the magnetic field in the three-dimensional kinematic dynamo problem when the boundary conditions and/or the external forcing are not isotropic. The velocity field is gaussian and $δ$-correlated in time, and its structure function scales with a positive exponent $ξ$. The covariance of the magnetic field is naturally computed as a sum of contributions proportional to the irreducible representations of the SO(3) symmetry group. The amplitudes are non-universal, determined by boundary conditions. The scaling exponents are universal, forming a discrete, strictly increasing spectrum indexed by the sectors of the symmetry group. When the initial mean magnetic field is zero, no dynamo effect is found, irrespective of the anisotropy of the forcing. The rate of isotropization with decreasing scales is fully understood from these results.

chao-dyn↗

arXiv1999

Exit time of turbulent signals: a way to detect the intermediate dissipative range

The exit time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (Inverse Structure Functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out that the Inverse Structure Functions show a much more extended Intermediate Dissipative Range than the Structure Functions, leading to the first clear evidence of the universal properties of such a range of scales.

chao-dyn↗

arXiv1999

Disentangling Scaling Properties in Anisotropic and Inhomogeneous Turbulence

We address scaling in inhomogeneous and anisotropic turbulent flows by decomposing structure functions into their irreducible representation of the SO(3) symmetry group which are designated by $j,m$ indices. Employing simulations of channel flows with Re$_λ\approx 70$ we demonstrate that different components characterized by different $j$ display different scaling exponents, but for a given $j$ these remain the same at different distances from the wall. The $j=0$ exponent agrees extremely well with high Re measurements of the scaling exponents, demonstrating the vitality of the SO(3) decomposition.

chao-dyn↗

arXiv1998

Multiscale velocity correlation in turbulence: experiments, numerical simulations, synthetic signals

Multiscale correlation functions in high Reynolds number experimental turbulence, numerical simulations and synthetic signals are investigated. Fusion Rules predictions as they arise from multiplicative, almost uncorrelated, random processes for the energy cascade are tested. Leading and sub-leading contribution, in the inertial range, can be explained as arising from a multiplicative random process for the energy transfer mechanisms. Two different predictions for correlations involving dissipative observable are also briefly discussed.

chao-dyn↗

arXiv1998

Multi-time, multi-scale correlation functions in turbulence and in turbulent models

A multifractal-like representation for multi-time multi-scale velocity correlation in turbulence and dynamical turbulent models is proposed. The importance of subleading contributions to time correlations is highlighted. The fulfillment of the dynamical constraints due to the equations of motion is thoroughly discussed. The prediction stemming from this representation are tested within the framework of shell models for turbulence.

chao-dyn↗

arXiv1998

Helicity advection in Turbulent Models

Helicity transfer in a shell model of turbulence is investigated. In particular, we study the scaling behavior of helicity transfer in a dynamical model of turbulence lacking inversion symmetry. We present some phenomenological and numerical support to the idea that Helicity becomes -at scale small enough- a passively-advected quantity.

chao-dyn↗

arXiv1998

Intermittency and eddy-viscosities in dynamical models of turbulence

The dependence of intermittent inertial properties on ultraviolet eddy viscosity closures is examined within the framework of shell-models of turbulent flows. Inertial intermittent exponents turn out to be fairly independent on the way energy is dissipated at small scales.

chao-dyn↗

arXiv1998

Multiscale velocity correlations in turbulence

Multiscale correlation functions in high Reynolds number experimental turbulence and synthetic signals are investigated. Fusion Rules predictions as they arise from multiplicative, almost uncorrelated, random processes for the energy cascade are tested. Leading and sub-leading contribution, in both the inertial and viscous ranges, are well captured by assuming a simple multiplicative random process for the energy transfer mechanisms.

chao-dyn↗

arXiv1997

Mimicking a turbulent signal: sequential multiaffine processes

An efficient method for the construction of a multiaffine process, with prescribed scaling exponents, is presented. At variance with the previous proposals, this method is sequential and therefore it is the natural candidate in numerical computations involving synthetic turbulence. The application to the realization of a realistic turbulent-like signal is discussed in detail. The method represents a first step towards the realization of a realistic spatio-temporal turbulent field.

chao-dyn↗

arXiv1997

Time-reversible Dynamical Systems for Turbulence

Dynamical Ensemble Equivalence between hydrodynamic dissipative equations and suitable time-reversible dynamical systems has been investigated in a class of dynamical systems for turbulence. The reversible dynamics is obtained from the original dissipative equations by imposing a global constraint. We find that, by increasing the input energy, the system changes from an equilibrium state to a non-equilibrium stationary state in which an energy cascade, with the same statistical properties of the original system, is clearly detected.

chao-dyn↗

arXiv1997

Helicity Transfer in Turbulent Models

Helicity transfer in a shell model of turbulence is investigated. We show that a Reynolds-independent helicity flux is present in the model when the large scale forcing breaks inversion symmetry. The equivalent in Shell Models of the ``2/15 law'', obtained from helicity conservation in Navier-Stokes eqs., is derived and tested. The odd part of helicity flux statistic is found to be dominated by a few very intense events. In a particular model, we calculate analytically leading and sub-leading contribution to the scaling of triple velocity correlation.

chao-dyn↗