Spectral approach to finite Reynolds number effects on Kolmogorov's 4/5 law in isotropic turbulence

International audienceThe Kolmogorov’s 4/5 law is often considered as the sole exact relationship of inertial range statistics. Its asymptotic character, however, has been evidenced, investigating the finite Reynolds number (FRN) effect for the third-order structure function S 3(r) (e.g., for longitudinal velocity increments with r separation length) using variants of the Kármán-Howarth equation in physical space. Similar semi-empirical fits were proposed for the maximum of the normalized structure function, C 3 = −max rS 3(r)/(ɛr), expressing C 3 − 4/5 as a power law of the Taylor-based Reynolds number. One of the most complete studies in this domain is by Antonia and Burratini [J. Fluid Mech. 550, 175 (2006)]. Considering that these studies are based on a model for the unsteady second-order structure function S 2(r,t), with no explicit model for the third-order structure function itself, we propose to revisit the FRN effect by a spectral approach, in the line of Qian [Phys. Rev. E 55, 337 (1997), Phys. Rev. E 60, 3409 (1999)]. The spectral transfer term T(k,t), from which S 3(r,t) is derived by an exact quadrature, is directly calculated by solving the Lin equation for the energy spectrum E(k,t), closed by a standard triadic (or three-point) theory, here Eddy Damped Quasi Normal Markovian. We show that the best spectral approach to the FRN effect is found by separately investigating the negative (largest scales) and positive (smaller scales) bumps of the transfer term, and not only by looking at the maximum of the spectral flux or maxk∫∞kT(p,t)dp→ɛ. In the forced case, previous results are well reproduced, with Reynolds numbers as high as Reλ  = 5 000 to nearly recover the 4/5 value. In the free decay case, the general trend is recovered as well, with an even higher value of Reλ  = 50 000, but the EDQNM plots are systematically below those in Antonia and Burattini [J. Fluid Mech. 550, 175 (2006)]. This is explained by the sensitivity to initial data for E(k) in solving the Lin equation at moderate Reynolds numbers. Accordingly, an ad hoc initialization yields results consistent with the experimental spectrum measurements of Comte-Bellot and Corrsin [J. Fluid Mech. 48(2), 273 (1971)], from which S 3(r) are recalculated. Present results show that the dispersion observed in existing data at low Reynolds number may be due to sensitivity to initial spectrum shape, a feature of the flow which is not under control in most of laboratory experiments

Recent advances on the top-down approach for modeling block copolymers.

2ème prix de la meilleure communication orale.International audienc

Global stability of the flow around a rotating sphere

The laminar flow past a fixed sphere rotating in the transverse direction with respect to the incoming uniform flow is investigated through both direct numerical simulations (DNS) and triglobal stability analysis. The stability features of the wake are analyzed as a function of the Reynolds number Re and the sphere dimensionless rotation rate Omega. The core of the instability is precisely located by using a sensitivity analysis. Results show the existence of two different unstable regions. Moreover, an asymptotic analysis is performed to study the imperfect pitchfork bifurcation originating at Re ~ 212 and the occurrence of a steady oblique path for the problem of a freely falling sphere

Consistent and Transferable Force Fields for Statistical Copolymer Systems at the Mesoscale

The statistical trajectory matching (STM) method was applied successfully to derive coarse grain (CG) models for bulk properties of homopolymers. The extension of the methodology for building CG models for statistical copolymer systems is much more challenging. We present here the strategy for developing CG models for styrene–butadiene–rubber, and we compare the quality of the resulting CG force fields on the structure and thermodynamics at different chemical compositions. The CG models are used through the use of a genuine mesoscopic method called the dissipative particle dynamics method and compared to high-resolution molecular dynamics simulations. We conclude that the STM method is able to produce coarse-grained potentials that are transferable in composition by using only a few reference systems. Additionally, this methodology can be applied on any copolymer system