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

Non Asymptotic Properties of Transport and Mixing

We study relative dispersion of passive scalar in non-ideal cases, i.e. in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than the domain size. Of course, in such a situation usual asymptotic quantities (the diffusion coefficients) do not give any relevant information about the transport mechanisms. On the other hand, we shall show that the Finite Size Lyapunov Exponent, originally introduced for the predictability problem, appears to be rather powerful in approaching the non-asymptotic transport properties. This technique is applied in a series of numerical experiments in simple flows with chaotic behaviors, in experimental data analysis of drifter and to study relative dispersion in fully developed turbulence.Comment: 19 RevTeX pages + 8 figures included, submitted on Chaos special issue on Transport and Mixin

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

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

Tumbling of polymers in semidilute solution under shear flow

The tumbling dynamics of individual polymers in semidilute solution is studied by large-scale non-equilibrium mesoscale hydrodynamic simulations. We find that the tumbling time is equal to the non-equilibrium relaxation time of the polymer end-to-end distance along the flow direction and strongly depends on concentration. In addition, the normalized tumbling frequency as well as the widths of the alignment distribution functions for a given concentration-dependent Weissenberg number exhibit a weak concentration dependence in the cross-over regime from a dilute to a semidilute solution. For semidilute solutions a universal behavior is obtained. This is a consequence of screening of hydrodynamic interactions at polymer concentrations exceeding the overlap concentration

Acceleration statistics of heavy particles in turbulence

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following the trajectories of up to 120 million particles with Stokes numbers, $St$, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: ({\it i}) The root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers; ({\it ii}) At a given $St$ the normalised acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers; ({\it iii}) The tails of the probability density function of the normalised acceleration $a/a_{\rm rms}$ decrease with $St$. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small $St$, and filtering induced by the particle response time, that takes over at larger $St$.Comment: 10 pages, 3 figs, 2 tables. A section with new results has been added. Revised version accepted for pubblication on Journal of Fluid Mechanic

Intermittency in two-dimensional Ekman-Navier-Stokes turbulence

We study the statistics of the vorticity field in two-dimensional Navier-Stokes turbulence with a linear Ekman friction. We show that the small-scale vorticity fluctuations are intermittent, as conjectured by Nam et al. [Phys. Rev. Lett. vol.84 (2000) 5134]. The small-scale statistics of vorticity fluctuations coincides with the one of a passive scalar with finite lifetime transported by the velocity field itself.Comment: 4 pages, 7 figure

On the terminal velocity of sedimenting particles in a flowing fluid

The influence of an underlying carrier flow on the terminal velocity of sedimenting particles is investigated both analytically and numerically. Our theoretical framework works for a general class of (laminar or turbulent) velocity fields and, by means of an ordinary perturbation expansion at small Stokes number, leads to closed partial differential equations (PDE) whose solutions contain all relevant information on the sedimentation process. The set of PDE's are solved by means of direct numerical simulations for a class of 2D cellular flows (static and time dependent) and the resulting phenomenology is analysed and discussed.Comment: 13 pages, 2 figures, submitted to JP

Nonlinear dynamics of the viscoelastic Kolmogorov flow

The weakly nonlinear regime of a viscoelastic Navier--Stokes fluid is investigated. For the purely hydrodynamic case, it is known that large-scale perturbations tend to the minima of a Ginzburg-Landau free-energy functional with a double-well (fourth-order) potential. The dynamics of the relaxation process is ruled by a one-dimensional Cahn--Hilliard equation that dictates the hyperbolic tangent profiles of kink-antikink structures and their mutual interactions. For the viscoelastic case, we found that the dynamics still admits a formulation in terms of a Ginzburg--Landau free-energy functional. For sufficiently small elasticities, the phenomenology is very similar to the purely hydrodynamic case: the free-energy functional is still a fourth-order potential and slightly perturbed kink-antikink structures hold. For sufficiently large elasticities, a critical point sets in: the fourth-order term changes sign and the next-order nonlinearity must be taken into account. Despite the double-well structure of the potential, the one-dimensional nature of the problem makes the dynamics sensitive to the details of the potential. We analysed the interactions among these generalized kink-antikink structures, demonstrating their role in a new, elastic instability. Finally, consequences for the problem of polymer drag reduction are presented.Comment: 26 pages, 17 figures, submitted to The Journal of Fluid Mechanic

Statistical geometry in scalar turbulence

A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized by strong clustering. The quantitative counterpart is the existence of special functions of particle configurations which are statistically invariant under the flow. These are the statistical integrals of motion controlling the scalar statistics at small scales and responsible for the breaking of scale invariance associated to intermittency.Comment: 4 pages, 5 figure