arXiv subjects

R. M. Pereira

Publications and source records attributed to R. M. Pereira.

13 recordsLinked to original sources

arXiv2026

The dynamical role of vortices in the two-dimensional inverse cascade of turbulence

We study the inverse energy cascade of two-dimensional turbulence by means of high-resolution numerical simulations forced at intermediate wavenumbers. To clarify the role of vortices generated near the forcing scale, we decompose the vorticity and velocity fields into vortex and background components. Although the vortex component carries only a small fraction of the total energy, it has a clear effect on the energy spectrum and produces deviations from dimensional Kolmogorov scaling, which is realized by the background flow. We derive a generalized von Karman--Howarth balance for the decomposed fields and obtain a relation involving the third-order correlation between vortex and background velocity increments. The simulations support this prediction, which we interpret as a constant inertial-range flux associated with vortex-background correlations.

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arXiv2025

Circulation Fluctuations of Elementary Turbulent Vortices

Thin vortex tubes, with core sizes within the dissipation range, profuse in a homogeneous and isotropic turbulent flow. Their intersections with an arbitrary plane define, as a mathematical construct, a dilute gas of localized, intermittently distributed, two-dimensional vortex spots. While their planar density fluctuations are described by a field-theoretical extension of log-normal single-point statistics, known as Gaussian multiplicative chaos (GMC), they carry circulations which are Gaussian-correlated throughout the inertial range. It is puzzling, then, to find that the circulations of individual vortices are fat-tailed distributed, an apparent paradox that we fix within the GMC framework. The solution, validated through the examination of direct numerical simulation data for a broad range of Reynolds numbers, unveils, as a surprising phenomenological result, an existing coupling between the circulation of vortex structures and the short-distance properties of their spatial distribution fluctuations at sub-Taylor microscales.

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arXiv2023

Vortex polarization and circulation statistics in isotropic turbulence

We carry out an in-depth analysis of a recently introduced vortex gas model of homogeneous and isotropic turbulence. Direct numerical simulations are used to provide a concrete physical interpretation of one of the model's constituent fields: the degree of vortex polarization. Our investigations shed light on the complexity underlying vortex interactions and reveal, furthermore, that despite some striking similarities, classical and quantum turbulence exhibit distinct structural characteristics, even at inertial range scales. Crucially, these differences arise due to correlations between the polarization and circulation intensity within vortex clusters.

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arXiv2022

Statistics of Extreme Turbulent Circulation Events from Multifractality Breaking

Recent numerical explorations of extremely intense circulation fluctuations at high Reynolds number flows have brought to light novel aspects of turbulent intermittency. Vortex gas modeling ideas, introduced alongside such developments, have led to accurate descriptions of the core and the intermediate tails of circulation probability distribution functions (cPDFs), as well as the scaling exponents associated to statistical moments of circulation. We extend the predictive reach of the vortex gas picture of turbulence, by emphasizing that multifractality breaking, one of its salient phenomenological ingredients, is the key concept to disclose the asymptotic form of cPDF tails. A remarkable analytical agreement is found with previous results derived within the framework of the instanton approach to circulation intermittency.

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arXiv2022

Eddy-Viscous Modeling and the Topology of Extreme Circulation Events in Three-Dimensional Turbulence

We discuss the role of particular velocity field configurations -- instantons, for short -- which are supposed to dominate the flow during the occurrence of extreme turbulent circulation events. Instanton equations, devised for the stochastic hydrodynamic setup of homogeneous and isotropic turbulence, are applied to the interpretation of direct numerical simulation results. We are able in this way to model the time evolution of extreme circulation events for a broad range of scales, through the combined use of eddy viscosity phenomenology and exact creeping instantons. While this approach works well for the core of circulation instantons, it fails to describe their tails. In order to overcome this difficulty, we put forward a numerical treatment of the axisymmetric instanton equations. Circulation instantons are then found to have a surprising topological structure, which consists of a system of paired counter-rotating vortex rings centered around the symmetry axis of a background axisymmetric vortical flow.

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arXiv2020

Vortex Gas Modeling of Turbulent Circulation Statistics

Statistical properties of circulation encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, as the dependence of circulation moments upon Reynolds numbers and length scales, and the specific shape of the heavy-tailed circulation probability distribution functions. We address these focal points in an investigation of circulation statistics for planar cuts of three-dimensional flows. The model introduced here borrows ideas from the structural approach to turbulence, whereby turbulent flows are depicted as dilute vortex gases, combined with the standard Obukhov-Kolmogorov phenomenological framework of small-scale intermittency. We are able to reproduce, in this way, key statistical features of circulation, in close agreement with empirical observations compiled from direct numerical simulations.

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arXiv2019

Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and vortex stretching, the form of the asymmetric heavy tails remain elusive. Here we describe the emergence of both properties through an exactly solvable stochastic model with a scale hierarchy of energy transfer rates. From a statistical superposition of a local equilibrium distribution weighted by a background density, the increments distribution is given by a novel class of skewed heavy-tailed distributions, written as a generalization of the Meijer $G$-functions. Excellent agreement in the multiscale scenario is found with numerical data of systems with different sizes and Reynolds numbers. Remarkably, the single scale limit provides poor fits to the background density, highlighting the central role of the multiscale mechanism. Our framework can be also applied to describe the challenging emergence of skewed distributions in complex systems.

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arXiv2019

The Onset of Intermittency in Stochastic Burgers Hydrodynamics

We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific velocity configurations - the viscous instantons - are assumed to play a dominant role in modeling the left tails of velocity gradient probability distribution functions. We find, as expected on general grounds, that the field theoretical approach becomes meaningful in practice only if the effects of fluctuations around instantons are taken into account. Working with a systematic cumulant expansion, it turns out that the integration of fluctuations yields, in leading perturbative order, to an effective description of the Burgers stochastic dynamics given by the renormalization of its associated heat kernel propagator and the external force-force correlation function.

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arXiv2018

Instantons and Fluctuations in a Lagrangian Model of Turbulence

We perform a detailed analytical study of the Recent Fluid Deformation (RFD) model for the onset of Lagrangian intermittency, within the context of the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. The model is based, as a key point, upon local closures for the pressure Hessian and the viscous dissipation terms in the stochastic dynamical equations for the velocity gradient tensor. We carry out a power counting hierarchical classification of the several perturbative contributions associated to fluctuations around the instanton-evaluated MSRJD action, along the lines of the cumulant expansion. The most relevant Feynman diagrams are then integrated out into the renormalized effective action, for the computation of velocity gradient probability distribution functions (vgPDFs). While the subleading perturbative corrections do not affect the global shape of the vgPDFs in an appreciable qualitative way, it turns out that they have a significant role in the accurate description of their non-Gaussian cores.

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arXiv2014

Velocity-Gradient Probability Distribution Functions in a Lagrangian Model of Turbulence

The Recent Fluid Deformation Closure (RFDC) model of lagrangian turbulence is recast in path-integral language within the framework of the Martin-Siggia-Rose functional formalism. In order to derive analytical expressions for the velocity-gradient probability distribution functions (vgPDFs), we carry out noise renormalization in the low-frequency regime and find approximate extrema for the Martin-Siggia-Rose effective action. We verify, with the help of Monte Carlo simulations, that the vgPDFs so obtained yield a close description of the single-point statistical features implied by the original RFDC stochastic differential equations.

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arXiv2013

Lattice Boltzmann method for bosons and fermions and the fourth order Hermite polynomial expansion

The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried until the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by J.Y. Yang et al through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded until fourth order in the Hermite polynomials.

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arXiv2013

Vorticity Statistics and the Time Scales of Turbulent Strain

Time scales of turbulent strain activity, denoted as the strain persistence times of first and second order, are obtained from time-dependent expectation values and correlation functions of lagrangian rate-of-strain eigenvalues taken in particularly defined statistical ensembles. Taking into account direct numerical simulation data, our approach relies on heuristic closure hypotheses which allow us to establish a connection between the statistics of vorticity and strain. It turns out that softly divergent prefactors correct the usual "1/s" strain time-scale estimate of standard turbulence phenomenology, in a way which is consistent with the phenomenon of vorticity intermittency.

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arXiv2009

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.

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