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R. Benzi

Publications and source records attributed to R. Benzi.

45 records · Page 3Linked to original sources
arXiv1997

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.

chao-dyn↗
arXiv1996

(1+1)-dimensional turbulence

A class of dynamical models of turbulence living on a one-dimensional dyadic-tree structure is introduced and studied. The models are obtained as a natural generalization of the popular GOY shell model of turbulence. These models are found to be chaotic and intermittent. They represent the first example of (1+1)-dimensional dynamical systems possessing non trivial multifractal properties. The dyadic structure allows to study spatial and temporal fluctuations. Energy dissipation statistics and its scaling properties are studied. Refined Kolmogorov Hypothesis is found to hold.

chao-dyn↗
arXiv1996

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, $λ$, is investigated. Intermittent corrections in the continuous limit of infinitely close shells ($λ\rightarrow 1$) 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.

chao-dyn↗
arXiv1995

Helical shell models for three dimensional turbulence

In this paper we study a new class of shell models, defined in terms of two complex dynamical variables per shell, transporting positive and negative helicity respectively. The dynamical equations are derived from a decomposition into helical modes of the velocity Fourier components of Navier-Stokes equations (F. Waleffe, Phys. Fluids A {\bf 4}, 350 (1992)). This decomposition leads to four different types of shell models, according to the possible non-equivalent combinations of helicities of the three interacting modes in each triad. Free parameters are fixed by imposing the conservation of energy and of a ``generalized helicity'' $H_α$ in the inviscid and unforced limit. For $α=1$ this non-positive invariant looks exactly like helicity in the Fourier-helical decomposition of the Navier-Stokes equations. Long numerical integrations are performed, allowing the computation of the scaling exponents of the velocity increments and energy flux moments. The dependence of the models on the generalized helicity parameter $α$ and on the scale parameter $λ$ is also studied. PDEs are finally derived in the limit when the ratio between shells goes to one.

chao-dyn↗
arXiv1995

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.

chao-dyn↗
arXiv1995

Extended Self Similarity in numerical simulations of 3D anisotropic turbulence

Using a code based on the Lattice Boltzmann Equation, we have performed numerical simulations of a turbulent shear flow. We investigate the scaling behaviour of the structure functions in presence of anisotropic homogeneous turbulence, and we show that although Extended Self Similarity does not hold when strong shear effects are present, a more generalized scaling law can still be defined.

chao-dyn↗
arXiv1995

A new scaling property of turbulent flows

We discuss a possible theoretical interpretation of the self scaling property of turbulent flows (Extended Self Similarity). Our interpretation predicts that, even in cases when ESS is not observed, a generalized self scaling, must be observed. This prediction is checked on a number of laboratory experiments and direct numerical simulations.

chao-dyn↗
arXiv1995

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.

chao-dyn↗