Related papers: Computing the Scaling Exponents in Fluid Turbulenc…
This manuscript is a draft of work in progress, meant for network distribution only. It will be updated to a formal preprint when the numerical calculations will be accomplished. In this draft we develop a consistent closure procedure for…
Elements of the analytic structure of anomalous scaling and intermittency in fully developed hydrodynamic turbulence are described. We focus here on the structure functions of velocity differences that satisfy inertial range scaling laws…
We present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of $N$ suitably coupled copies of the "Sabra" shell…
In paper I of this series on fluid turbulence we showed that exact resummations of the perturbative theory of the structure functions of velocity differences result in a finite (order by order) theory. These findings exclude any known…
From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the…
In anisotropic turbulence the correlation functions are decomposed in the irreducible representations of the SO(3) symmetry group (with different "angular momenta" $\ell$). For different values of $\ell$ the second order correlation…
In this paper we derive here, on the basis of the NS eqs. a set of fusion rules for correlations of velocity differences when all the separation are in the inertial interval. Using this we consider the standard hierarchy of equations…
The anomalous scaling exponents $\zeta_{n}$ of the longitudinal structure functions $S_{n}$ for homogeneous isotropic turbulence are derived from the Navier-Stokes equations by using field theoretic methods to develop a low energy…
On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit…
A recent discovery about the inertial range of homogeneous and isotropic turbulence is the saturation of the scaling exponents $\zeta_n$ for large $n$, defined via structure functions of order $n$ as $S_{n}(r)=\overline{(\delta_r…
The scale dependent intermittency exponents in developed hydrodynamic turbulence are calculated assuming a natural hierarchy of correlations in the turbulence. The major correlations are taken into account explicitly, while the remaining…
The main difficulty of statistical theories of fluid turbulence is the lack of an obvious small parameter. In this paper we show that the formerly established fusion rules can be employed to develop a theory in which Kolmogorov's statistics…
To characterize fluctuations in a turbulent flow, one usually studies different moments of velocity increments and dissipation rate, $\overline{(v(x+r)-v(x))^{n}}\propto r^{\zeta_{n}}$ and $\overline{{\cal E}^{n}}\propto Re^{d_{n}}$,…
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…
It is shown that the idea that scaling behavior in turbulence is limited by one outer length $L$ and one inner length $\eta$ is untenable. Every n'th order correlation function of velocity differences $\bbox{\cal F}_n(\B.R_1,\B.R_2,\dots)$…
The scaling properties of three-dimensional magnetohydrodynamic turbulence are obtained from direct numerical simulations of decaying turbulence using $512^3$ modes. The results indicate that the turbulence does not follow the…
An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following…
It is shown that statistical properties of developed hydrodynamic turbulence are characterized by an infinite set of independent anomalous exponents which describes the scaling behavior of hydrodynamic fields constructed from the second and…
We analyse the scaling properties of the energy spectra in fully developed incompressible turbulence in forced, rotating fluids in three dimensions (3D), which are believed to be characterised by universal scaling exponents in the inertial…
The scaling properties of correlation functions of non-scalar fields (constructed from velocity derivatives) in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. It is explained that these exponents also…