Local 4/5-Law and Energy Dissipation Anomaly in Turbulence

A strong local form of the ``4/3-law'' in turbulent flow has been proved recently by Duchon and Robert for a triple moment of velocity increments averaged over both a bounded spacetime region and separation vector directions, and for energy dissipation averaged over the same spacetime region. Under precisely stated hypotheses, the two are proved to be proportional, by a constant 4/3, and to appear as a nonnegative defect measure in the local energy balance of singular (distributional) solutions of the incompressible Euler equations. Here we prove that the energy defect measure can be represented also by a triple moment of purely longitudinal velocity increments and by a mixed moment with one longitudinal and two tranverse velocity increments. Thus, we prove that the traditional 4/5- and 4/15-laws of Kolmogorov hold in the same local sense as demonstrated for the 4/3-law by Duchon-Robert.Comment: 14 page

Scaling Analysis and Evolution Equation of the North Atlantic Oscillation Index Fluctuations

The North Atlantic Oscillation (NAO) monthly index is studied from 1825 till 2002 in order to identify the scaling ranges of its fluctuations upon different delay times and to find out whether or not it can be regarded as a Markov process. A Hurst rescaled range analysis and a detrended fluctuation analysis both indicate the existence of weakly persistent long range time correlations for the whole scaling range and time span hereby studied. Such correlations are similar to Brownian fluctuations. The Fokker-Planck equation is derived and Kramers-Moyal coefficients estimated from the data. They are interpreted in terms of a drift and a diffusion coefficient as in fluid mechanics. All partial distribution functions of the NAO monthly index fluctuations have a form close to a Gaussian, for all time lags, in agreement with the findings of the scaling analyses. This indicates the lack of predictive power of the present NAO monthly index. Yet there are some deviations for large (and thus rare) events. Whence suggestions for other measurements are made if some improved predictability of the weather/climate in the North Atlantic is of interest. The subsequent Langevin equation of the NAO signal fluctuations is explicitly written in terms of the diffusion and drift parameters, and a characteristic time scale for these is given in appendix.Comment: 6 figures, 54 refs., 16 pages; submitted to Int. J. Mod. Phys. C: Comput. Phy

Constraining the neutrino magnetic moment with anti-neutrinos from the Sun

We discuss the impact of different solar neutrino data on the spin-flavor-precession (SFP) mechanism of neutrino conversion. We find that, although detailed solar rates and spectra allow the SFP solution as a sub-leading effect, the recent KamLAND constraint on the solar antineutrino flux places stronger constraints to this mechanism. Moreover, we show that for the case of random magnetic fields inside the Sun, one obtains a more stringent constraint on the neutrino magnetic moment down to the level of \mu_\nu \lsim few \times 10^{-12}\mu_B, similar to bounds obtained from star cooling.Comment: 4 pages, 3 figures. Final version to appear in Phys. Rev. Let

On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators

In this note we study the approach to equilibrium of a chain of anharmonic oscillators. We find indications that a sufficiently large system always relaxes to the usual equilibrium distribution. There is no sign of an ergodicity threshold. The time however to arrive to equilibrium diverges when $g \to 0$, $g$ being the anharmonicity.Comment: 8 pages, 5 figure

Log-Poisson Cascade Description of Turbulent Velocity Gradient Statistics

The Log-Poisson phenomenological description of the turbulent energy cascade is evoked to discuss high-order statistics of velocity derivatives and the mapping between their probability distribution functions at different Reynolds numbers. The striking confirmation of theoretical predictions suggests that numerical solutions of the flow, obtained at low/moderate Reynolds numbers can play an important quantitative role in the analysis of experimental high Reynolds number phenomena, where small scales fluctuations are in general inaccessible from direct numerical simulations

Interactions of a Light Hypersonic Jet with a Non-Uniform Interstellar Medium

We present three dimensional simulations of the interaction of a light hypersonic jet with an inhomogeneous thermal and turbulently supported disk in an elliptical galaxy. We model the jet as a light, supersonic non-relativistic flow with parameters selected to be consistent with a relativistic jet with kinetic power just above the FR1/FR2 break. We identify four generic phases in the evolution of such a jet with the inhomogeneous interstellar medium: 1) an initial ``flood and channel'' phase, where progress is characterized by high pressure gas finding changing weak points in the ISM, flowing through channels that form and re-form over time, 2) a spherical, energy-driven bubble phase, were the bubble is larger than the disk scale, but the jet remains fully disrupted close to the nucleus, 3) a rapid, jet break--out phase the where jet breaks free of the last dense clouds, becomes collimated and pierces the spherical bubble, and 4) a classical phase, the jet propagates in a momentum-dominated fashion leading to the classical jet + cocoon + bow-shock structure. Mass transport in the simulations is investigated, and we propose a model for the morphology and component proper motions in the well-studied Compact Symmetric Object 4C31.04.Comment: 66 pages, 22 figures, PDFLaTeX, aastex macros, graphicx and amssymb packages, Accepted, to be published 2007 ApJ

Considerations on bubble fragmentation models

n this paper we describe the restrictions that the probability density function (p.d.f.) of the size of particles resulting from the rupture of a drop or bubble must satisfy. Using conservation of volume, we show that when a particle of diameter, D0, breaks into exactly two fragments of sizes D and D2 = (D30−D3)1/3 respectively, the resulting p.d.f., f(D; D0), must satisfy a symmetry relation given by D22 f(D; D0) = D2 f(D2; D0), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D0), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D0) ∫0D0 (D/D0)3 f(D; D0) dD = 1. A detailed analysis of some contemporary fragmentation models shows that they may not exhibit the required conservation of volume condition if they are not adequately formulated. Furthermore, we also analyse several models proposed in the literature for the breakup frequency of drops or bubbles based on different principles, g(ϵ, D0). Although, most of the models are formulated in terms of the particle size D0 and the dissipation rate of turbulent kinetic energy, ϵ, and apparently provide different results, we show here that they are nearly identical when expressed in dimensionless form in terms of the Weber number, g*(Wet) = g(ϵ, D0) D2/30 ϵ−1/3, with Wet ~ ρ ϵ2/3 D05/3/σ, where ρ is the density of the continuous phase and σ the surface tension

Turbulent luminance in impassioned van Gogh paintings

We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation

Degree of randomness: numerical experiments for astrophysical signals

Astrophysical and cosmological signals such as the cosmic microwave background radiation, as observed, typically contain contributions of different components, and their statistical properties can be used to distinguish one from the other. A method developed originally by Kolmogorov is involved for the study of astrophysical signals of randomness of various degrees. Numerical performed experiments based on the universality of Kolmogorov distribution and using a single scaling of the ratio of stochastic to regular components, reveal basic features in the behavior of generated signals also in terms of a critical value for that ratio, thus enable the application of this technique for various observational datasetsComment: 6 pages, 9 figures; Europhys.Letters; to match the published versio

Intermittency in the Joint Cascade of Energy and Helicity

The statistics of the energy and helicity fluxes in isotropic turbulence are studied using high resolution direct numerical simulation. The scaling exponents of the energy flux agree with those of the transverse velocity structure functions through refined similarity hypothesis, consistent with Kraichnan's prediction \cite{Kr74}. The helicity flux is even more intermittent than the energy flux and its scaling exponents are closer to those of the passive scalar. Using Waleffe's helical decomposition, we demonstrate that the existence of positive mean helicity flux inhibits the energy transfer in the negative helical modes, a non-passive effect