L. Moriconi

Large-scale intermittency in the atmospheric boundary layer

We find actual evidence, relying upon vorticity time series taken in a high-Reynolds-number atmospheric experiment, that to a very good approximation the surface boundary layer flow may be described, in a statistical sense and under certain regimes, as an advected ensemble of homogeneous turbulent systems, characterized by a log-normal distribution of fluctuating intensities. Our analysis suggests that the usual direct numerical simulations of homogeneous and isotropic turbulence, performed at moderate Reynolds numbers, may play an important role in the study of turbulent boundary layer flows, if supplemented with appropriate statistical information concerned with the structure of large-scale fluctuations.

Statistics of intense turbulent vorticity events.

We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term correlated at large scales, we obtain in the high Reynolds number regime a closed analytical expression for the probability distribution function of an arbitrary component of the vorticity field. The central idea underlying the analysis consists in the restriction of the velocity configurational phase-space to a particular sector where the rate of strain and the rotation tensors can be locally regarded as slow and fast degrees of freedom, respectively. This prescription is implemented along the Martin-Siggia-Rose functional framework, whereby instantons and perturbations around them are taken into account within a steepest-descent approach.

Conformal invariance in (2+1)-dimensional stochastic systems.

Stochastic partial differential equations can be used to model second-order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and some are indeed proved) to be described by conformal field theories. We advance, in the framework of the Martin-Siggia-Rose field-theoretical formalism of stochastic dynamics, a general solution of the translation Ward identities, which yields a putative conformal energy-momentum tensor. Even though the computation of energy-momentum correlators is obstructed, in principle, by dimensional reduction issues, these are bypassed by the addition of replicated fields to the original (2+1)-dimensional model. The method is illustrated with an application to the Kardar-Parisi-Zhang (KPZ) model of surface growth. The consistency of the approach is checked by means of a straightforward perturbative analysis of the KPZ ultraviolet region, leading, as expected, to its c=1 conformal fixed point.

Extended self-similarity in the two-dimensional metal-insulator transition

We show that extended self-similarity, a scaling phenomenon first observed in classical turbulent flows, holds for a two-dimensional metal-insulator transition that belongs to the universality class of random Dirac fermions. Deviations from multifractality, which in turbulence are due to the dominance of diffusive processes at small scales, appear in the condensed-matter context as a large-scale, finite-size effect related to the imposition of an infrared cutoff in the field theory formulation. We propose a phenomenological interpretation of extended self-similarity in the metal-insulator transition within the framework of the random beta-model description of multifractal sets. As a natural step, our discussion is bridged to the analysis of strange attractors, where crossovers between multifractal and nonmultifractal regimes are found and extended self-similarity turns out to be verified as well.

Langevin simulation of the chirally decomposed sine-Gordon model.

A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-Abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte Carlo methods are useless in dealing with these models, alternative computational strategies have been proposed along the years. The Langevin technique, in particular, is known to be frequently plagued with difficulties such as strong numerical instabilities or subtle ergodic behavior. Regarding the chirally decomposed version of the sine-Gordon model as a prototypical case for the failure of the Langevin approach, we devise a truncation prescription in the stochastic differential equations which yields numerical stability and is assumed not to spoil the Berezinskii-Kosterlitz-Thouless transition. This conjecture is supported by a finite size scaling analysis, whereby a massive phase ending at a line of critical points is clearly observed for the truncated stochastic model.

Vortex reconnection as the dissipative scattering of dipoles

We propose a phenomenological model of vortex tube reconnection at high Reynolds numbers. The basic picture is that squeezed vortex lines, formed by stretching in the region of closest approach between filaments, interact like dipoles (monopole-antimonopole pairs) of a confining electrostatic theory. The probability of dipole creation is found from a canonical ensemble spanned by foldings of the vortex tubes, with temperature parameter estimated from the typical energy variation taking place in the reconnection process. Vortex line reshuffling by viscous diffusion is described in terms of directional transitions of the dipoles. The model is used to fit with reasonable accuracy experimental data established long ago on the symmetric collision of vortex rings. We also study along similar lines the asymmetric case, related to the reconnection of non-parallel vortex tubes.

Minimalist turbulent boundary layer model.

We discuss an elementary model of a turbulent boundary layer over a flat surface given as a vertical random distribution of spanwise Lamb-Oseen vortex configurations placed over a nonslip boundary-condition line. We are able to reproduce several important features of realistic flows, such as the viscous and logarithmic boundary sublayers, and the general behavior of the first statistical moments (turbulent intensity, skewness, and flatness) of the streamwise velocity fluctuations. As an application, we advance some heuristic considerations on the boundary layer underlying kinematics that could be associated with the phenomenon of drag reduction by polymers, finding a suggestive support from its experimental signatures.

Log-Poisson cascade description of turbulent velocity-gradient statistics.

The Log-Poisson phenomenological description of the turbulent energy cascade is evoked to discuss high-order statistics of velocity derivatives and the mapping between their probability distribution functions at different Reynolds numbers. The striking confirmation of theoretical predictions suggests that numerical solutions of the flow obtained at low/moderate Reynolds numbers can play an important quantitative role in the analysis of experimental high Reynolds number phenomena, where small scales fluctuations are in general inaccessible from direct numerical simulations.

Instanton theory of Burgers shocks and intermittency

A Lagrangian approach to Burgers turbulence is carried out along the lines of the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics. We derive, from an analysis based on the hypothesis of unbroken Galilean invariance, the asymptotic form of the probability distribution function of negative velocity differences. The origin of Burgers intermittency is found to rely on the dynamical coupling between shocks, identified to instantons, and noncoherent background fluctuations, which-then-cannot be discarded in a consistent statistical description of the flow.

Stochastic perturbations in vortex-tube dynamics

A dual lattice vortex formulation of homogeneous turbulence is developed, within the Martin-Siggia-Rose field theoretical approach. It consists of a generalization of the usual dipole version of the Navier-Stokes equations, known to hold in the limit of vanishing external forcing. We investigate, as a straightforward application of our formalism, the dynamics of closed vortex tubes, randomly stirred at large length scales by Gaussian stochastic forces. We find that besides the usual self-induced propagation, the vortex tube evolution may be effectively modeled through the introduction of an additional white-noise correlated velocity field background. The resulting phenomenological picture is closely related to observations previously reported from a wavelet decomposition analysis of turbulent flow configurations.