Anisotropic Homogeneous Turbulence: hierarchy and intermittency of scaling exponents in the anisotropic sectors

We present the first measurements of anisotropic statistical fluctuations in perfectly homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors and hierarchical ordering of anisotropies on a direct numerical simulation of a three dimensional random Kolmogorov flow. We achieved an homogeneous and anisotropic statistical ensemble by randomly shifting the forcing phases. We observe high intermittency as a function of the order of the velocity correlation within each fixed anisotropic sector and a hierarchical organization of scaling exponents at fixed order of the velocity correlation at changing the anisotropic sector.Comment: 6 pages, 3 eps figure

The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer

The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model.They containcontributions from various 2d and 3d aspects, and from the superposition ofinhomogeneous and anisotropic contributions. We employ the recently introduceddecomposition of statistical tensor objects into irreducible representations of theSO(3) symmetry group (characterized by $j$ and $m$ indices), to disentangle someof these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different $j$ contributions transform differently under rotations and so form a complete basis in which to represent the tensor objects under study. The experimental data arerecorded with hot-wire probes placed at various heights in the atmospheric surfacelayer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by $j=0$, $j=1$ and $j=2$. The analysis shows the need to make a careful distinction between long-lived quasi 2d turbulent motions (close to the ground) and relatively short-lived 3d motions. We demonstrate that the leading scaling exponents in the three leading sectors ($j = 0, 1, 2$) appear to be different butuniversal, independent of the positions of the probe, and the large scaleproperties. The measured values of the exponent are $\zeta^{(j=0)}_2=0.68 \pm 0.01$, $\zeta^{(j=1)}_2=1.0\pm 0.15$ and $\zeta^{(j=2)}_2=1.38 \pm 0.10$. We present theoretical arguments for the values of these exponents usingthe Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML) version of this paper is avaliable at http://lvov.weizmann.ac.il

Statistics of pressure and of pressure-velocity correlations in isotropic turbulence

Some pressure and pressure-velocity correlation in a direct numerical simulations of a three-dimensional turbulent flow at moderate Reynolds numbers have been analyzed. We have identified a set of pressure-velocity correlations which posseses a good scaling behaviour. Such a class of pressure-velocity correlations are determined by looking at the energy-balance across any sub-volume of the flow. According to our analysis, pressure scaling is determined by the dimensional assumption that pressure behaves as a ``velocity squared'', unless finite-Reynolds effects are overwhelming. The SO(3) decompositions of pressure structure functions has also been applied in order to investigate anisotropic effects on the pressure scaling.Comment: 21 pages, 8 figur

Statistical conservation laws in turbulent transport

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. We propose that with very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments (without forcing the transported fields) we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas

Eulerian Statistically Preserved Structures in Passive Scalar Advection

We analyze numerically the time-dependent linear operators that govern the dynamics of Eulerian correlation functions of a decaying passive scalar advected by a stationary, forced 2-dimensional Navier-Stokes turbulence. We show how to naturally discuss the dynamics in terms of effective compact operators that display Eulerian Statistically Preserved Structures which determine the anomalous scaling of the correlation functions. In passing we point out a bonus of the present approach, in providing analytic predictions for the time-dependent correlation functions in decaying turbulent transport.Comment: 10 pages, 10 figures. Submitted to Phys. Rev.

Inhomogeneous Anisotropic Passive Scalars

We investigate the behaviour of the two-point correlation function in the context of passive scalars for non homogeneous, non isotropic forcing ensembles. Exact analytical computations can be carried out in the framework of the Kraichnan model for each anisotropic sector. It is shown how the homogeneous solution is recovered at separations smaller than an intrinsic typical lengthscale induced by inhomogeneities, and how the different Fourier modes in the centre-of-mass variable recombine themselves to give a ``beating'' (superposition of power laws) described by Bessel functions. The pure power-law behaviour is restored even if the inhomogeneous excitation takes place at very small scales.Comment: 14 pages, 5 figure

Derivative moments in turbulent shear flows

We propose a generalized perspective on the behavior of high-order derivative moments in turbulent shear flows by taking account of the roles of small-scale intermittency and mean shear, in addition to the Reynolds number. Two asymptotic regimes are discussed with respect to shear effects. By these means, some existing disagreements on the Reynolds number dependence of derivative moments can be explained. That odd-order moments of transverse velocity derivatives tend not vanish as expected from elementary scaling considerations does not necessarily imply that small-scale anisotropy persists at all Reynolds numbers.Comment: 11 pages, 7 Postscript figure