相关论文: Anomalous Scaling and Fusion Rules in Hydrodynamic…

We show that the Kolmogorov-1941 picture of fully developed hydrodynamic turbulence (with the scaling of the structure functions $S_n(R) \propto R^{n/3}$) necessarily leads to an anomalous scaling for correlation functions which include the…

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…

Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…

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…

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…

The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this Letter we introduce a shell model of turbulence that exhibits anomalous scaling with a tunable small…

The original goal of Large Eddy Simulations of fully developed turbulent flows was to accurately describe large-scale flow features ${\bf u}(\Delta)$ at the scales $r\geq \Delta$ where $\Delta$ is a size of computational mesh. The effect 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 $\bbox{\cal F}_n(\B.R_1,\B.R_2,\dots)$…

Anomalous scaling in the statistics of an active scalar in homogeneous turbulent convection is studied using a dynamical shell model. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent…

We construct multi-mode viscous hydrodynamics for one dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales)…

We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group. In this approach, scaling properties are related to the fixed…

The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully…

A synopsis of an analytical theory of scaling in developed turbulence is proposed on the basis of the Navier-Stokes equations. It is shown that corrections to the normal Kolmogorov 1941 scaling behavior of the $n$-th order velocity…

It is shown that the description of anomalous scaling in turbulent systems requires the simultaneous use of two normalization scales. This phenomenon stems from the existence of two independent (infinite) sets of anomalous scaling exponents…

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian,…

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…

We present a numerical study of anisotropic statistical fluctuations in homogeneous turbulent flows. We give an argument to predict the dimensional scaling exponents, (p+j)/3, for the projections of p-th order structure function in the j-th…

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…

We show that multiscaling properties of developed turbulence in shell models, which lead to anomalous scaling exponents in the inertial range, are determined exclusively by instanton dynamics. Instantons represent correlated extreme events…

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…