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M Vergassola

Publications and source records attributed to M Vergassola.

10 recordsLinked to original sources
PubMed2002

Intermittency in two-dimensional Ekman-Navier-Stokes turbulence.

We study the statistics of the vorticity field in two-dimensional Navier-Stokes turbulence with linear Ekman friction. We show that the small-scale vorticity fluctuations are intermittent, as conjectured by Bernard [Europhys. Lett. 50, 333 (2000)] and Nam et al. [Phys. Rev. Lett. 84, 5134 (2000)]. The small-scale statistics of vorticity fluctuations coincide with that of a passive scalar with finite lifetime transported by the velocity field itself.

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PubMed2001

Statistical conservation laws in turbulent transport.

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. With very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas.

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PubMed2001

Universal decay of scalar turbulence.

The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the scalar-generally non-Gaussian-with global self-similar evolution in time. Analogous behavior is found numerically with a more realistic flow resulting from an inverse energy cascade.

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PubMed2001

Statistical geometry in scalar turbulence.

A general link between geometry and intermittency in passive scalar turbulence is established. The anomalous part of the scalar correlation functions is shown to be dominated by special functions of particle configurations. Their major property is that those functions calculated along the particle trajectories remain statistically constant in time. Those conservation laws qualitatively imply the persistence of scalar particles in strongly clustered geometries.

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PubMed2000

Universality and saturation of intermittency in passive scalar turbulence

The statistical properties of a scalar field advected by the nonintermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are probed by comparing the results obtained with two types of injection mechanisms. Scaling properties are shown to be universal, even though anisotropies injected at large scales persist down to the smallest scales and local isotropy is not fully restored. Scalar statistics is strongly intermittent and scaling exponents saturate to a constant for sufficiently high orders. This is observed also for the advection by a velocity field rapidly changing in time, pointing to the genericity of the phenomenon.

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PubMed2000

Inverse energy cascade in two-dimensional turbulence: deviations from gaussian behavior

High-resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussian behavior of velocity differences statistics are quantitatively investigated. The level of statistical convergence is pushed enough to permit reliable measurement of the asymmetries in the probability distribution functions of longitudinal increments and odd-order moments, which bring the signature of the inverse energy flux. No measurable intermittency corrections could be found in their scaling laws. The seventh order skewness increases by almost two orders of magnitude with respect to the third, thus becoming of order unity.

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