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.Comment: 12 pages, 5 eps figure

Homogeneous and Isotropic Turbulence: a short survey on recent developments

We present a detailed review of some of the most recent developments on Eulerian and Lagrangian turbulence in homogeneous and isotropic statistics. In particular, we review phenomenological and numerical results concerning the issue of universality with respect to the large scale forcing and the viscous dissipative physics. We discuss the state-of-the-art of numerical versus experimental comparisons and we discuss the dicotomy between phenomenology based on coherent structures or on statistical approaches. A detailed discussion of finite Reynolds effects is also presented.Comment: based on the talk presented by R. Benzi at DSFD 2-14. postprint version, published online on 6 July 2015 J. Stat. Phy

On the intermittent energy transfer at viscous scales in turbulent flows

In this letter we present numerical and experimental results on the scaling properties of velocity turbulent fields in the range of scales where viscous effects are acting. A generalized version of Extended Self Similarity capable of describing scaling laws of the velocity structure functions down to the smallest resolvable scales is introduced. Our findings suggest the absence of any sharp viscous cutoff in the intermittent transfer of energy.Comment: 10 pages, plain Latex, 6 figures available upon request to [email protected]

Universal statistics of non-linear energy transfer in turbulent models

A class of shell models for turbulent energy transfer at varying the inter-shell separation, $\lambda$, is investigated. Intermittent corrections in the continuous limit of infinitely close shells ($\lambda \rightarrow 1$) have been measured. Although the model becomes, in this limit, non-intermittent, we found universal aspects of the velocity statistics which can be interpreted in the framework of log-poisson distributions, as proposed by She and Waymire (1995, Phys. Rev. Lett. 74, 262). We suggest that non-universal aspects of intermittency can be adsorbed in the parameters describing statistics and properties of the most singular structure. On the other hand, universal aspects can be found by looking at corrections to the monofractal scaling of the most singular structure. Connections with similar results reported in other shell models investigations and in real turbulent flows are discussed.Comment: 4 pages, 2 figures available upon request to [email protected]

Generalized scaling in fully developed turbulence

In this paper we report numerical and experimental results on the scaling properties of the velocity turbulent fields in several flows. The limits of a new form of scaling, named Extended Self Similarity(ESS), are discussed. We show that, when a mean shear is absent, the self scaling exponents are universal and they do not depend on the specific flow (3D homogeneous turbulence, thermal convection , MHD). In contrast, ESS is not observed when a strong shear is present. We propose a generalized version of self scaling which extends down to the smallest resolvable scales even in cases where ESS is not present. This new scaling is checked in several laboratory and numerical experiment. A possible theoretical interpretation is also proposed. A synthetic turbulent signal having most of the properties of a real one has been generated.Comment: 25 pages, plain Latex, figures are available upon request to the authors ([email protected], [email protected]

A lattice Boltzmann study of non-hydrodynamic effects in shell models of turbulence

A lattice Boltzmann scheme simulating the dynamics of shell models of turbulence is developed. The influence of high order kinetic modes (ghosts) on the dissipative properties of turbulence dynamics is studied. It is analytically found that when ghost fields relax on the same time scale as the hydrodynamic ones, their major effect is a net enhancement of the fluid viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve on a much longer time scale. Analytical results are borne out by high-resolution numerical simulations. These simulations indicate that the hydrodynamic manifold is very robust towards large fluctuations of non hydrodynamic fields.Comment: 17 pages, 3 figures, submitted to Physica

Stochastic Resonance in Two Dimensional Landau Ginzburg Equation

We study the mechanism of stochastic resonance in a two dimensional Landau Ginzburg equation perturbed by a white noise. We shortly review how to renormalize the equation in order to avoid ultraviolet divergences. Next we show that the renormalization amplifies the effect of the small periodic perturbation in the system. We finally argue that stochastic resonance can be used to highlight the effect of renormalization in spatially extended system with a bistable equilibria

Analytic calculation of anomalous scaling in random shell models for a passive scalar

An exact non-perturbative calculation of the fourth-order anomalous correction to the scaling behaviour of a random shell-model for passive scalars is presented. Importance of ultraviolet (UV) and infrared (IR) boundary conditions on the inertial scaling properties are determined. We find that anomalous behaviour is given by the null-space of the inertial operator and we prove strong UV and IR independence of the anomalous exponent. A limiting case where diffusive behaviour can influence inertial properties is also presented.Comment: 3 pages, 1 figure, revised versio

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.Comment: 15 pages, 6 figure