On the Rapid Increase of Intermittency in the Near-Dissipation Range of Fully Developed Turbulence

Intermittency, measured as log(F(r)/3), where F(r) is the flatness of velocity increments at scale r, is found to rapidly increase as viscous effects intensify, and eventually saturate at very small scales. This feature defines a finite intermediate range of scales between the inertial and dissipation ranges, that we shall call near-dissipation range. It is argued that intermittency is multiplied by a universal factor, independent of the Reynolds number Re, throughout the near-dissipation range. The (logarithmic) extension of the near-dissipation range varies as \sqrt(log Re). As a consequence, scaling properties of velocity increments in the near-dissipation range strongly depend on the Reynolds number.Comment: 7 pages, 7 figures, to appear in EPJ

A Stochastic Representation of the Local Structure of Turbulence

Based on the mechanics of the Euler equation at short time, we show that a Recent Fluid Deformation (RFD) closure for the vorticity field, neglecting the early stage of advection of fluid particles, allows to build a 3D incompressible velocity field that shares many properties with empirical turbulence, such as the teardrop shape of the R-Q plane. Unfortunately, non gaussianity is weak (i.e. no intermittency) and vorticity gets preferentially aligned with the wrong eigenvector of the deformation. We then show that slightly modifying the former vectorial field in order to impose the long range correlated nature of turbulence allows to reproduce the main properties of stationary flows. Doing so, we end up with a realistic incompressible, skewed and intermittent velocity field that reproduces the main characteristics of 3D turbulence in the inertial range, including correct vorticity alignment properties.Comment: 6 pages, 3 figures, final version, published

Recent Fluid Deformation closure for velocity gradient tensor dynamics in turbulence: time-scale effects and expansions

In order to model pressure and viscous terms in the equation for the Lagrangian dynamics of the velocity gradient tensor in turbulent flows, Chevillard & Meneveau (Phys. Rev. Lett. 97, 174501, 2006) introduced the Recent Fluid Deformation closure. Using matrix exponentials, the closure allows to overcome the unphysical finite-time blow-up of the well-known Restricted Euler model. However, it also requires the specification of a decorrelation time scale of the velocity gradient along the Lagrangian evolution, and when the latter is chosen too short (or, equivalently, the Reynolds number is too high), the model leads to unphysical statistics. In the present paper, we explore the limitations of this closure by means of numerical experiments and analytical considerations. We also study the possible effects of using time-correlated stochastic forcing instead of the previously employed white-noise forcing. Numerical experiments show that reducing the correlation time scale specified in the closure and in the forcing does not lead to a commensurate reduction of the autocorrelation time scale of the predicted evolution of the velocity gradient tensor. This observed inconsistency could explain the unrealistic predictions at increasing Reynolds numbers.We perform a series expansion of the matrix exponentials in powers of the decorrelation time scale, and we compare the full original model with a linearized version. The latter is not able to extend the limits of applicability of the former but allows the model to be cast in terms of a damping term whose sign gives additional information about the stability of the model as function of the second invariant of the velocity gradient tensor.Comment: 11 pages, 14 figures, submitted to the special issue "Fluids and Turbulence" of Physica

Orientation dynamics of small, triaxial-ellipsoidal particles in isotropic turbulence

The orientation dynamics of small anisotropic tracer particles in turbulent flows is studied using direct numerical simulation (DNS) and results are compared with Lagrangian stochastic models. Generalizing earlier analysis for axisymmetric ellipsoidal particles (Parsa et al. 2012), we measure the orientation statistics and rotation rates of general, triaxial ellipsoidal tracer particles using Lagrangian tracking in DNS of isotropic turbulence. Triaxial ellipsoids that are very long in one direction, very thin in another, and of intermediate size in the third direction exhibit reduced rotation rates that are similar to those of rods in the ellipsoid's longest direction, while exhibiting increased rotation rates that are similar to those of axisymmetric discs in the thinnest direction. DNS results differ significantly from the case when the particle orientations are assumed to be statistically independent from the velocity gradient tensor. They are also different from predictions of a Gaussian process for the velocity gradient tensor, which does not provide realistic preferred vorticity-strain-rate tensor alignments. DNS results are also compared with a stochastic model for the velocity gradient tensor based on the recent fluid deformation approximation (RFDA). Unlike the Gaussian model, the stochastic model accurately predicts the reduction in rotation rate in the longest direction of triaxial ellipsoids since this direction aligns with the flow's vorticity, with its rotation perpendicular to the vorticity being reduced. For disc-like particles, or in directions perpendicular to the longest direction in triaxial particles, the model predicts {noticeably} smaller rotation rates than those observed in DNS, a behavior that can be understood based on the probability of vorticity orientation with the most contracting strain-rate eigen-direction in the model.Comment: 24 pages, 15 color figures, references added, published versio

Multiple precision evaluation of the Airy Ai function with reduced cancellation

The series expansion at the origin of the Airy function Ai(x) is alternating and hence problematic to evaluate for x > 0 due to cancellation. Based on a method recently proposed by Gawronski, M\"uller, and Reinhard, we exhibit two functions F and G, both with nonnegative Taylor expansions at the origin, such that Ai(x) = G(x)/F(x). The sums are now well-conditioned, but the Taylor coefficients of G turn out to obey an ill-conditioned three-term recurrence. We use the classical Miller algorithm to overcome this issue. We bound all errors and our implementation allows an arbitrary and certified accuracy, that can be used, e.g., for providing correct rounding in arbitrary precision

On the two lists of 'four [types of] words' (/nāṟ‐col/) in the śāstric descriptions of Tamil

The research for this article, which falls under the general category "History of Linguistics", was started as an examination, in context, of the use of the Tamil technical term tiricol, lit. "mutant word", which is the designation of the second among four categories of "word(s)" (col) inside one of the two quadripartite classificatory systems, found in the Tolkāppiyam, an ancient Tamil śāstric text, probably dating back to the first half of the first millenium AD. The first term in that quadripartition is iyaṟ‐col "natural word", whereas the third and the fourth are ticai‐c‐col "regional word(s)" and vaṭacol "northern word(s)"

Unified Multifractal Description of Velocity Increments Statistics in Turbulence: Intermittency and Skewness

The phenomenology of velocity statistics in turbulent flows, up to now, relates to different models dealing with either signed or unsigned longitudinal velocity increments, with either inertial or dissipative fluctuations. In this paper, we are concerned with the complete probability density function (PDF) of signed longitudinal increments at all scales. First, we focus on the symmetric part of the PDFs, taking into account the observed departure from scale invariance induced by dissipation effects. The analysis is then extended to the asymmetric part of the PDFs, with the specific goal to predict the skewness of the velocity derivatives. It opens the route to the complete description of all measurable quantities, for any Reynolds number, and various experimental conditions. This description is based on a single universal parameter function D(h) and a universal constant R*.Comment: 13 pages, 3 figures, Extended version, Publishe

The use of polysemy for word‐play in ancient Tamil literature and the traditional tools available for dealing with it.

This text is the written version of an oral communication which was presented (in English) at the Colloquium "Sens multiple(s) et polysémie : perspectives croisées, Orient & Occident [http://polysemie2013.ugrenoble3.fr/] in Aix‐en‐Provence [4th‐ 6th June 2013], organized by Sylvain Brocquet, Julie Sorba and Christophe Cusimano. A French translation of this text will appear in issue 35 of the Études Romanes de Brno (ISSN 1803‐7399).This presentation will serve a double purpose. On the one hand, I shall present excerpts from ancient Tamil literature, illustrating the use of polysemy (and homophony), in combination with "dignified puns" 1 in a poem which came to be called Tiruviyamaka "sacred yamaka" by posterity, after the name of an ornamental figure (aṇi) which that poem seems (perhaps anachronistically) to illustrate, that figure belonging to a type called yamaka (in Sanskrit) or maṭakku (in Tamil) by later theoreticians. On the other hand, I shall briefly discuss some lexical tools created in the course of the twin histories of Tamil "classical"2 literature(s) and Tamil śāstric literature(s), and transmitted up to the present time by many successive generations of teachers and students, the transmission process itself being probably responsible for the progressive growth and multiplication of those tools, often referred to as kōśa‐s "thesauri", the two most ancient Tamil kōśa‐s being the Tivākaram and the Piṅkalam, which certainly played an important role in codifying and mapping literary Tamil