The large-scale structure of passive scalar turbulence

We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field. At scales larger than the characteristic lengthscale of scalar injection, yet smaller than the correlation length of the velocity, the advected field displays persistent long-range correlations due to the underlying turbulent velocity. These induce significant deviations from equilibrium statistics for high-order scalar correlations, despite the absence of scalar flux.Comment: 4 pages, 6 figure

Scaling and universality in turbulent convection

Anomalous correlation functions of the temperature field in two-dimensional turbulent convection are shown to be universal with respect to the choice of external sources. Moreover, they are equal to the anomalous correlations of the concentration field of a passive tracer advected by the convective flow itself. The statistics of velocity differences is found to be universal, self-similar and close to Gaussian. These results point to the conclusion that temperature intermittency in two-dimensional turbulent convection may be traced back to the existence of statistically preserved structures, as it is in passive scalar turbulence.Comment: 4 pages, 6 figure

Relative dispersion in fully developed turbulence: from Eulerian to Lagrangian statistics in synthetic flows

The effect of Eulerian intermittency on the Lagrangian statistics of relative dispersion in fully developed turbulence is investigated. A scaling range spanning many decades is achieved by generating a multi-affine synthetic velocity field with prescribed intermittency features. The scaling laws for the Lagrangian statistics are found to depend on Eulerian intermittency in agreement with a multifractal description. As a consequence of the Kolmogorov's law, the Richardson's law for the variance of pair separation is not affected by intermittency corrections.Comment: 4 pages RevTeX, 4 PostScript figure

The predictability problem in systems with an uncertainty in the evolution law

The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many characteristic times and scales. The importance of a proper parameterization of fast scales in systems with many strongly interacting degrees of freedom is highlighted and its consequences for the modelization of geophysical systems are discussed.Comment: 20 pages RevTeX, 6 eps figures (included

Pair dispersion in synthetic fully developed turbulence

The Lagrangian statistics of relative dispersion in fully developed turbulence is numerically investigated. A scaling range spanning many decades is achieved by generating a synthetic velocity field with prescribed Eulerian statistical features. When the velocity field obeys Kolmogorov similarity, the Lagrangian statistics is self similar too, and in agreement with Richardson's predictions. For an intermittent velocity field the scaling laws for the Lagrangian statistics are found to depend on Eulerian intermittency in agreement with a multifractal description. As a consequence of the Kolmogorov law the Richardson law for the variance of pair separation is not affected by intermittency corrections. A new analysis method, based on fixed scale averages instead of usual fixed time statistics, is shown to give much wider scaling range and should be preferred for the analysis of experimental data.Comment: 9 pages, 9 ps figures, submitted to Physics of Fluid

Monotonic Distributive Semilattices

In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; ArgentinaFil: Menchón, María Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Mimicking a turbulent signal: sequential multiaffine processes

An efficient method for the construction of a multiaffine process, with prescribed scaling exponents, is presented. At variance with the previous proposals, this method is sequential and therefore it is the natural candidate in numerical computations involving synthetic turbulence. The application to the realization of a realistic turbulent-like signal is discussed in detail. The method represents a first step towards the realization of a realistic spatio-temporal turbulent field.Comment: 4 pages, 3 figures (included), RevTeX 3.