Multiple-scale analysis and renormalization for pre-asymptotic scalar transport

Pre-asymptotic transport of a scalar quantity passively advected by a velocity field formed by a large-scale component superimposed to a small-scale fluctuation is investigated both analytically and by means of numerical simulations. Exploiting the multiple-scale expansion one arrives at a Fokker--Planck equation which describes the pre-asymptotic scalar dynamics. Such equation is associated to a Langevin equation involving a multiplicative noise and an effective (compressible) drift. For the general case, no explicit expression for both the effective drift and the effective diffusivity (actually a tensorial field) can be obtained. We discuss an approximation under which an explicit expression for the diffusivity (and thus for the drift) can be obtained. Its expression permits to highlight the important fact that the diffusivity explicitly depends on the large-scale advecting velocity. Finally, the robustness of the aforementioned approximation is checked numerically by means of direct numerical simulations.Comment: revtex4, 12 twocolumn pages, 3 eps figure

Large-scale effects on meso-scale modeling for scalar transport

The transport of scalar quantities passively advected by velocity fields with a small-scale component can be modeled at meso-scale level by means of an effective drift and an effective diffusivity, which can be determined by means of multiple-scale techniques. We show that the presence of a weak large-scale flow induces interesting effects on the meso-scale scalar transport. In particular, it gives rise to non-isotropic and non-homogeneous corrections to the meso-scale drift and diffusivity. We discuss an approximation that allows us to retain the second-order effects caused by the large-scale flow. This provides a rather accurate meso-scale modeling for both asymptotic and pre-asymptotic scalar transport properties. Numerical simulations in model flows are used to illustrate the importance of such large-scale effects.Comment: 19 pages, 8 figure

Large-scale confinement and small-scale clustering of floating particles in stratified turbulence

We study the motion of small inertial particles in stratified turbulence. We derive a simplified model, valid within the Boussinesq approximation, for the dynamics of small particles in presence of a mean linear density profile. By means of extensive direct numerical simulations, we investigate the statistical distribution of particles as a function of the two dimensionless parameters of the problem. We find that vertical confinement of particles is mainly ruled by the degree of stratification, with a weak dependency on the particle properties. Conversely, small scale fractal clustering, typical of inertial particles in turbulence, depends on the particle relaxation time and is almost independent on the flow stratification. The implications of our findings for the formation of thin phytoplankton layers are discussed.Comment: 5 pages, 6 figure

Bank Accounting Standards in Mexico. A layman’s guide to changes 10 years after the 1995 bank crisis

After the 1995 crisis, the Mexican banking system experienced significant changes in bank accounting standards. Most of these changes took place between 1996 and 2001, and had a significant impact in the structure and interpretation of financial information of banks. This document explains the major changes on bank accounting, their purpose and structure, and discusses their impact on financial information reported by Mexican banks. It also provides the English equivalent of the major accounting terms used by Mexican banks. The main purpose of this document is to provide a standardized guide to better understand financial information produced before and after the crisis, within the current context of internationalization of Mexican banks' ownership.

Clustering and collisions of heavy particles in random smooth flows

Finite-size impurities suspended in incompressible flows distribute inhomogeneously, leading to a drastic enhancement of collisions. A description of the dynamics in the full position-velocity phase space is essential to understand the underlying mechanisms, especially for polydisperse suspensions. These issues are here studied for particles much heavier than the fluid by means of a Lagrangian approach. It is shown that inertia enhances collision rates through two effects: correlation among particle positions induced by the carrier flow and uncorrelation between velocities due to their finite size. A phenomenological model yields an estimate of collision rates for particle pairs with different sizes. This approach is supported by numerical simulations in random flows.Comment: 12 pages, 9 Figures (revTeX 4) final published versio

Statistics of mixing in three-dimensional Rayleigh--Taylor turbulence at low Atwood number and Prandtl number one

Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a paradigmatic time-dependent turbulent system in which the integral scale grows in time following the evolution of the mixing region. In order to fully characterize the statistical properties of the flow, both temporal and spatial behavior of relevant statistical indicators have been analyzed. Scaling of both global quantities ({\it e.g.}, Rayleigh, Nusselt and Reynolds numbers) and scale dependent observables built in terms of velocity and temperature fluctuations are considered. We extend the mean-field analysis for velocity and temperature fluctuations to take into account intermittency, both in time and space domains. We show that the resulting scaling exponents are compatible with those of classical Navier--Stokes turbulence advecting a passive scalar at comparable Reynolds number. Our results support the scenario of universality of turbulence with respect to both the injection mechanism and the geometry of the flow

Relaxation of finite perturbations: Beyond the Fluctuation-Response relation

We study the response of dynamical systems to finite amplitude perturbation. A generalized Fluctuation-Response relation is derived, which links the average relaxation toward equilibrium to the invariant measure of the system and points out the relevance of the amplitude of the initial perturbation. Numerical computations on systems with many characteristic times show the relevance of the above relation in realistic cases.Comment: 7 pages, 5 figure

Microfósiles calcáreos no-marinos del cretácico superior en Zampal, provincia de Mendoza, Argentina

Fil: Uliana, Miguel A.. Yacimientos Petrolíferos Fiscales; ArgentinaFil: Musacchio, Eduardo. Facultad de Ciencias Naturales y Museo; Argentin

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