A LES-Langevin model for turbulence

We propose a new model of turbulence for use in large-eddy simulations (LES). The turbulent force, represented here by the turbulent Lamb vector, is divided in two contributions. The contribution including only subfilter fields is deterministically modeled through a classical eddy-viscosity. The other contribution including both filtered and subfilter scales is dynamically computed as solution of a generalized (stochastic) Langevin equation. This equation is derived using Rapid Distortion Theory (RDT) applied to the subfilter scales. The general friction operator therefore includes both advection and stretching by the resolved scale. The stochastic noise is derived as the sum of a contribution from the energy cascade and a contribution from the pressure. The LES model is thus made of an equation for the resolved scale, including the turbulent force, and a generalized Langevin equation integrated on a twice-finer grid. The model is validated by comparison to DNS and is tested against classical LES models for isotropic homogeneous turbulence, based on eddy viscosity. We show that even in this situation, where no walls are present, our inclusion of backscatter through the Langevin equation results in a better description of the flow.Comment: 18 pages, 14 figures, to appear in Eur. Phys. J.

Statistical optimization for passive scalar transport: maximum entropy production vs maximum Kolmogorov-Sinay entropy

We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov-Sinai entropy using a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov-Sinai entropy seen as functions of f admit a unique maximum denoted fmaxEP and fmaxKS. The behavior of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this article is that fmaxEP and fmaxKS have the same Taylor expansion at _rst order in the deviation of equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP (N) tends towards a non-zero value, while fmaxKS (N) tends to 0 when N goes to infinity. For values of N typical of that adopted by Paltridge and climatologists we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N_ such that fmaxEP and fmaxKS coincide, at least up to a second order parameter proportional to the non-equilibrium uxes imposed to the boundaries.Comment: Nonlinear Processes in Geophysics (2015

Interferometric molecular line observations of W51

Observations are presented of the H II region complex in W51 made with a mm interferometer. W51 is a region of massive star formation approx. 7 kpc distant from the sun. This region has been well studied in both the IR and submillimeter, the radio, as well as the maser transitions. These previous observations have revealed three regions of interest: (1) W51MAIN, a know of bright maser emission near two compact H II regions W51e1 and W51e2 (W51MAIN is also the peak of the 400 micron emission indicating that the bulk of the mass is centered there; (2) W51IRS1 is a long curving structure seen at 20 micron and at 2 and 6 cm but not at 400 micron; (3) W51IRS2 (also known as W51NORTH) is another compact H II region slightly offset from an 8 and a 20 micron peak and a collection of masers. Some conclusions are as follows: (1) SO and H(13)CN emission are similar and coincide with outflow activity; (2) HCO+ spectra show evidence for overall collapse of the W51 cloud toward W51MAIN; (3) A previously undetected continuum peak, W51DUST, coincides with the molecular peak H(13)CN-4; and (4) Dust emission at 3.4 mm reveals that about half of the 400 micron emission comes from the ultracompact H II region e2, and the rest from W51e1 and W51DUST

Multi-fractality, universality and singularity in turbulence

International audienceIn most geophysical flows, vortices (or eddies) of all sizes are observed. In 1941, Kolmogorov devised a theory to describe the hierarchical organization of such vortices via a homogeneous self-similar process. This theory correctly explains the universal power-law energy spectrumobserved in all turbulent flows. Finer observations however prove that this picture is too simplistic, owing to intermittency of energy dissipation and high velocity derivatives. In this review, we discuss how such intermittency can be explained and fitted into a new picture of turbulence. We first discuss how the concept of multi-fractality (invented by Parisi and Frisch in 1982) enables to generalize the concept of self-similarity in a non-homogeneous environment and recover a universality in turbulence. We further review the local extension of this theory, and show how it enables to probe the most irregular locations of the velocity field, in the sense foreseen by Lars Onsager in 1949. Finally, we discuss how the multi-fractal theory connects to possible singularities, in the real or in the complex plane, as first investigated by Frisch and Morf in 1981

Instabilites, turbulence et transport dans les disques d'accretion par methodes asymptotiques

INIST T 75686 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Au-delà des cascades de Kolmogorov

The large-scale structure of many turbulent flows encountered in practical situations such as aeronautics, industry, meteorology is nowadays successfully computed using the Kolmogorov-Karman-Howarth energy cascade picture. This theory appears increasingly inaccurate when going down the energy cascade, that terminates through intermittent spots of energy dissipation, at variance with the assumed homogeneity. This is problematic for the modeling of all processes that depend on small scales of turbulence, such as combustion instabilities or droplet atomization in industrial burners or cloud formation. This paper explores a paradigm shift where the homogeneity hypothesis is replaced by the assumption that turbulence contains singularities, as suggested by Onsager. This paradigm leads to a weak formulation of the Kolmogorov-Karman-Howarth-Monin equation (WKHE) that allows taking into account explicitly the presence of singularities and their impact on the energy transfer and dissipation. It provides a local in scale, space and time description of energy transfers and dissipation, valid for any inhomogeneous, anisotropic flow, under any type of boundary conditions. The goal of this article is to discuss WKHE as a tool to get a new description of energy cascades and dissipation that goes beyond Kolmogorov and allows the description of small-scale intermittency. It puts the problem of intermittency and dissipation in turbulence into a modern framework, compatible with recent mathematical advances on the proof of Onsager's conjecture

Asymptotic ultimate regime of homogeneous Rayleigh–Bénard convection on logarithmic lattices

International audienceWe investigate how the heat flux $Nu$ scales with the imposed temperature gradient $Ra$ in homogeneous Rayleigh–Bénard convection using one-, two- and three-dimensional simulations on logarithmic lattices. Logarithmic lattices are a new spectral decimation framework which enables us to span an unprecedented range of parameters ( $Ra$ , $Re$ , $\Pr$ ) and test existing theories using little computational power. We first show that known diverging solutions can be suppressed with a large-scale friction. In the turbulent regime, for $\Pr \approx 1$ , the heat flux becomes independent of viscous processes (‘asymptotic ultimate regime’, $Nu\sim Ra ^{1/2}$ with no logarithmic correction). We recover scalings coherent with the theory developed by Grossmann and Lohse, for all situations where the large-scale frictions keep a constant magnitude with respect to viscous and diffusive dissipation. We also identify another turbulent friction-dominated regime at $\Pr \ll 1$ , where deviations from the Grossmann and Lohse prediction are observed. These two friction-dominated regimes may be relevant in some geophysical or astrophysical situations, where large-scale friction arises due to rotation, stratification or magnetic field