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]

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

Saturation of Turbulent Drag Reduction in Dilute Polymer Solutions

Drag reduction by polymers in turbulent wall-bounded flows exhibits universal and non-universal aspects. The universal maximal mean velocity profile was explained in a recent theory. The saturation of this profile and the crossover back to the Newtonian plug are non-universal, depending on Reynolds number Re, concentration of polymer $c_p$ and the degree of polymerization $N_p$. We explain the mechanism of saturation stemming from the finiteness of extensibility of the polymers, predict its dependence on $c_p$ and $N$ in the limit of small $c_p$ and large Re, and present the excellent comparison of our predictions to experiments on drag reduction by DNA.Comment: 4 pages, 4 figs., included, PRL, submitte

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.Comment: Plain Latex, 1 figure available upon request to [email protected]

Mean- Field Approximation and Extended Self-Similarity in Turbulence

Recent experimental discovery of extended self-similarity (ESS) was one of the most interesting developments, enabling precise determination of the scaling exponents of fully developed turbulence. Here we show that the ESS is consistent with the Navier-Stokes equations, provided the pressure -gradient contributions are expressed in terms of velocity differences in the mean field approximation (Yakhot, Phys.Rev. E{\bf 63}, 026307, (2001)). A sufficient condition for extended self-similarity in a general dynamical systemComment: 8 pages, no figure

Scaling and Dissipation in the GOY Shell Model

This is a paper about multi-fractal scaling and dissipation in a shell model of turbulence, called the GOY model. This set of equations describes a one dimensional cascade of energy towards higher wave vectors. When the model is chaotic, the high-wave-vector velocity is a product of roughly independent multipliers, one for each logarithmic momentum shell. The appropriate tool for studying the multifractal properties of this model is shown to be the energy current on each shell rather than the velocity on each shell. Using this quantity, one can obtain better measurements of the deviations from Kolmogorov scaling (in the GOY dynamics) than were available up to now. These deviations are seen to depend upon the details of inertial-range structure of the model and hence are {\em not} universal. However, once the conserved quantities of the model are fixed to have the same scaling structure as energy and helicity, these deviations seem to depend only weakly upon the scale parameter of the model. We analyze the connection between multifractality in the velocity distribution and multifractality in the dissipation. Our arguments suggest that the connection is universal for models of this character, but the model has a different behavior from that of real turbulence. We also predict the scaling behavior of time correlations of shell-velocities, of the dissipation,Comment: Revised Versio

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

Observations on degenerate saddle point problems

We investigate degenerate saddle point problems, which can be viewed as limit cases of standard mixed formulations of symmetric problems with large jumps in coefficients. We prove that they are well-posed in a standard norm despite the degeneracy. By wellposedness we mean a stable dependence of the solution on the right-hand side. A known approach of splitting the saddle point problem into separate equations for the primary unknown and for the Lagrange multiplier is used. We revisit the traditional Ladygenskaya--Babu\v{s}ka--Brezzi (LBB) or inf--sup condition as well as the standard coercivity condition, and analyze how they are affected by the degeneracy of the corresponding bilinear forms. We suggest and discuss generalized conditions that cover the degenerate case. The LBB or inf--sup condition is necessary and sufficient for wellposedness of the problem with respect to the Lagrange multiplier under some assumptions. The generalized coercivity condition is necessary and sufficient for wellposedness of the problem with respect to the primary unknown under some other assumptions. We connect the generalized coercivity condition to the positiveness of the minimum gap of relevant subspaces, and propose several equivalent expressions for the minimum gap. Our results provide a foundation for research on uniform wellposedness of mixed formulations of symmetric problems with large jumps in coefficients in a standard norm, independent of the jumps. Such problems appear, e.g., in numerical simulations of composite materials made of components with contrasting properties.Comment: 8 page

Intermittency and structure functions in channel flow turbulence

We present a study of intermittency in a turbulent channel flow. Scaling exponents of longitudinal streamwise structure functions, $\zeta_p /\zeta_3$, are used as quantitative indicators of intermittency. We find that, near the center of the channel the values of $\zeta_p /\zeta_3$ up to $p=7$ are consistent with the assumption of homogeneous/isotropic turbulence. Moving towards the boundaries, we observe a growth of intermittency which appears to be related to an intensified presence of ordered vortical structures. In fact, the behaviour along the normal-to-wall direction of suitably normalized scaling exponents shows a remarkable correlation with the local strength of the Reynolds stress and with the \rms value of helicity density fluctuations. We argue that the clear transition in the nature of intermittency appearing in the region close to the wall, is related to a new length scale which becomes the relevant one for scaling in high shear flows.Comment: 4 pages, 6 eps figure