Intermittency and universality in a Lagrangian model of velocity gradients in three-dimensional turbulence

The universality of intermittency in hydrodynamic turbulence is considered based on a recent model for the velocity gradient tensor evolution. Three possible versions of the model are investigated differing in the assumed correlation time-scale and forcing strength. Numerical tests show that the same (universal) anomalous relative scaling exponents are obtained for the three model variants. It is also found that transverse velocity gradients are more intermittent than longitudinal ones, whereas dissipation and enstrophy scale with the same exponents. The results are consistent with the universality of intermittency and relative scaling exponents, and suggest that these are dictated by the self-stretching terms that are the same in each variant of the model

Gaussian multiplicative Chaos for symmetric isotropic matrices

Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy

Lagrangian dynamics and statistical geometric structure of turbulence

The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The non-local pressure and viscous effects are accounted for by a closure that models the material deformation history of fluid elements. The resulting stochastic system reproduces many statistical and geometric trends observed in numerical and experimental 3D turbulent flows, including anomalous relative scaling.Comment: 5 pages, 5 figures, final version, publishe

Probing quantum and classical turbulence analogy through global bifurcations in a von K\'arm\'an liquid Helium experiment

We report measurements of the dissipation in the Superfluid Helium high REynold number von Karman flow (SHREK) experiment for different forcing conditions, through a regime of global hysteretic bifurcation. Our macroscopical measurements indicate no noticeable difference between the classical fluid and the superfluid regimes, thereby providing evidence of the same dissipative anomaly and response to asymmetry in fluid and superfluid regime. %In the latter case, A detailed study of the variations of the hysteretic cycle with Reynolds number supports the idea that (i) the stability of the bifurcated states of classical turbulence in this closed flow is partly governed by the dissipative scales and (ii) the normal and the superfluid component at these temperatures (1.6K) are locked down to the dissipative length scale.Comment: 5 pages, 5 figure

Fully developed turbulence and the multifractal conjecture

We review the Parisi-Frisch MultiFractal formalism for Navier--Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.Comment: Special Issue dedicated to E. Brezin and G. Paris

Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq

International audienceThe verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of generic tools such as computer algebra systems. In fact, the inherent difficulty of computing such bounds often mandates a formal proof of them. In this paper, we present a tactic for the Coq proof assistant that is designed to automatically and formally prove bounds on univariate expressions. It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions. All the computations are performed inside Coq's logic, in a reflexive setting. This paper also compares our tactic with various existing tools on a large set of examples

Spin-Glass Model for Inverse Freezing

We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction displaying the inverse freezing phenomenon. The behaviour of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and spinodal lines for the model are computed using the Full Replica Symmetry Breaking Ansatz that always yelds a thermodynamically stable phase. We compare the results both with the quenched disordered model with Ising spins on lattice gas - where no reentrance takes place - and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. 93, 037202 (2004)]. The simplest version of all these models, known as Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase, including the right thermodynamic behavior.Comment: 6 pages, 4 figures, to appear in the Proceeding for the X International Workshop on Disordered Systems (2006), Molveno, Ital

Seasonal, synoptic, and diurnal-scale variability of biogeochemical trace gases and O2 from a 300-m tall tower in central Siberia

We present first results from 19 months of semicontinuous concentration measurements of biogeochemical trace gases (CO2, CO, and CH4) and O2, measured at the Zotino Tall Tower Observatory (ZOTTO) in the boreal forest of central Siberia. We estimated CO2 and O2 seasonal cycle amplitudes of 26.6 ppm and 134 per meg, respectively. An observed west-east gradient of about -7 ppm (in July 2006) between Shetland Islands, Scotland, and ZOTTO reflects summertime continental uptake of CO2 and is consistent with regional modeling studies. We found the oceanic component of the O2 seasonal amplitude (Atmospheric Potential Oxygen, or APO) to be 51 per meg, significantly smaller than the 95 per meg observed at Shetlands, illustrating a strong attenuation of the oceanic O2 signal in the continental interior. Comparison with the Tracer Model 3 (TM3) atmospheric transport model showed good agreement with the observed phasing and seasonal amplitude in CO2; however, the model exhibited greater O2 (43 per meg, 32%) and smaller APO (9 per meg, 18%) amplitudes. This seeming inconsistency in model comparisons between O2 and APO appears to be the result of phasing differences in land and ocean signals observed at ZOTTO, where ocean signals have a significant lag. In the first 2 months of measurements on the fully constructed tower (November and December 2006), we observed several events with clear vertical concentration gradients in all measured species except CO. During “cold events” (below -30°C) in November 2006, we observed large vertical gradients in CO2 (up to 22 ppm), suggesting a strong local source. The same pattern was observed in CH4 concentrations for the same events. Diurnal vertical CO2 gradients in April to May 2007 gave estimates for average nighttime respiration fluxes of 0.04 ± 0.02 mol C m-2 d-1, consistent with earlier eddy covariance measurements in 1999–2000 in the vicinity of the tower

Acceleration and vortex filaments in turbulence

We report recent results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We present some results concerning acceleration statistics and the statistics of trapping by vortex filaments.Comment: 10 pages, 5 figure