The decay of homogeneous anisotropic turbulence

We present the results of a numerical investigation of three-dimensional decaying turbulence with statistically homogeneous and anisotropic initial conditions. We show that at large times, in the inertial range of scales: (i) isotropic velocity fluctuations decay self-similarly at an algebraic rate which can be obtained by dimensional arguments; (ii) the ratio of anisotropic to isotropic fluctuations of a given intensity falls off in time as a power law, with an exponent approximately independent of the strength of the fluctuation; (iii) the decay of anisotropic fluctuations is not self-similar, their statistics becoming more and more intermittent as time elapses. We also investigate the early stages of the decay. The different short-time behavior observed in two experiments differing by the phase organization of their initial conditions gives a new hunch on the degree of universality of small-scale turbulence statistics, i.e. its independence of the conditions at large scales.Comment: 9 pages, 17 figure

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

Anisotropy in Homogeneous Rotating Turbulence

The effective stress tensor of a homogeneous turbulent rotating fluid is anisotropic. This leads us to consider the most general axisymmetric four-rank ``viscosity tensor'' for a Newtonian fluid and the new terms in the turbulent effective force on large scales that arise from it, in addition to the microscopic viscous force. Some of these terms involve couplings to vorticity and others are angular momentum non conserving (in the rotating frame). Furthermore, we explore the constraints on the response function and the two-point velocity correlation due to axisymmetry. Finally, we compare our viscosity tensor with other four-rank tensors defined in current approaches to non-rotating anisotropic turbulence.Comment: 14 pages, RevTe

Mean value coordinates–based caricature and expression synthesis

We present a novel method for caricature synthesis based on mean value coordinates (MVC). Our method can be applied to any single frontal face image to learn a specified caricature face pair for frontal and 3D caricature synthesis. This technique only requires one or a small number of exemplar pairs and a natural frontal face image training set, while the system can transfer the style of the exemplar pair across individuals. Further exaggeration can be fulfilled in a controllable way. Our method is further applied to facial expression transfer, interpolation, and exaggeration, which are applications of expression editing. Additionally, we have extended our approach to 3D caricature synthesis based on the 3D version of MVC. With experiments we demonstrate that the transferred expressions are credible and the resulting caricatures can be characterized and recognized

Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents

The first example of a turbulent system where the failure of the hypothesis of small-scale isotropy restoration is detectable both in the `flattening' of the inertial-range scaling exponent hierarchy, and in the behavior of odd-order dimensionless ratios, e.g., skewness and hyperskewness, is presented. Specifically, within the kinematic approximation in magnetohydrodynamical turbulence, we show that for compressible flows, the isotropic contribution to the scaling of magnetic correlation functions and the first anisotropic ones may become practically indistinguishable. Moreover, skewness factor now diverges as the P\'eclet number goes to infinity, a further indication of small-scale anisotropy.Comment: 4 pages Latex, 1 figur

Completeness of classical spin models and universal quantum computation

We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence of an inhomogeneous magnetic field, can specialize to the partition function of any Ising system on an arbitrary graph. In this sense the 2D Ising model is said to be "complete". However, in order to obtain the above result, the coupling strengths on the 2D lattice must assume complex values, and thus do not allow for a physical interpretation. Here we show how a complete model with real -and, hence, "physical"- couplings can be obtained if the 3D Ising model is considered. We furthermore show how to map general q-state systems with possibly many-body interactions to the 2D Ising model with complex parameters, and give completeness results for these models with real parameters. We also demonstrate that the computational overhead in these constructions is in all relevant cases polynomial. These results are proved by invoking a recently found cross-connection between statistical mechanics and quantum information theory, where partition functions are expressed as quantum mechanical amplitudes. Within this framework, there exists a natural correspondence between many-body quantum states that allow universal quantum computation via local measurements only, and complete classical spin systems.Comment: 43 pages, 28 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

Strong Universality in Forced and Decaying Turbulence

The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents {\em and} the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is also the case for Navier-Stokes turbulence.Comment: RevTex 4, 10 pages, 5 Figures (included), 1 Table; PRE, submitte

Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group

The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we firstly consider the needed general theory and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.Comment: 35 pages, REVTEX, 1 figure, Phys. Rev. E, submitte