Rodrigo Miranda Pereira

Universidade Federal Fluminense | UFF · Departamento de Física (GFI)

We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incom-pressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stre...

We develop a stochastic model for the velocity gradients dynamics along a Lagrangian trajectory. Comparing with different attempts proposed in the literature, the present model, at the cost of introducing a free parameter known in turbulence phenomenology as the intermittency coefficient, gives a realistic picture of velocity gradient statistics at...

The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function is computed along with the most probable path in the weak noise limit through the saddle-point appro...

It is well known that solutions to the Fourier-Galerkin truncation of the inviscid Burgers equation (and other hyperbolic conservation laws) do not converge to the physically relevant entropy solution after the formation of the first shock. This loss of convergence was recently studied in detail in [S. S. Ray et al., Phys. Rev. E 84, 016301 (2011)]...

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 r...

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, which are related to a picture of turbulence as a dilute system of vortex tube structures, have been introduced alongside such developments, leading to a...

Adaptive Galerkin methods for time-dependent partial differential equations are studied and shown to be dissipative. The adaptation implies that the subset of the selected basis function changes over time according to the evolution of the solution. The corresponding projection operator is thus time-dependent and non differentiable. We therefore pro...

The small-scale statistical properties of velocity circulation in classical homogeneous and isotropic turbulent flows are assessed through a modeling framework that brings together the multiplicative cascade and the structural descriptions of turbulence. We find that vortex structures exhibit short-distance repulsive correlations, which is evidence...

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 numer...

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 num...

The small-scale statistical properties of velocity circulation in classical homogeneous and isotropic turbulent flows are assessed through a modeling framework that brings together the multiplicative cascade and the structural descriptions of turbulence. We find that vortex structures exhibit short-distance repulsive correlations, which is evidence...

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...

We study dynamical Galerkin schemes for evolutionary partial differential equations (PDEs), where the projection operator changes over time. When selecting a subset of basis functions, the projection operator is non-differentiable in time and an integral formulation has to be used. We analyze the projected equations with respect to existence and un...

Realizamos um sobrevoo abrangente sobre a teoria estatística da turbulência, com a preocupação de embasá-la em noções importantes e consolidadas da dinâmica de fluidos, antes de nos aprofundarmos em discussões de modelos mais específicos, sujeitos a debates contemporâneos. A complexidade da turbulência traduz-se, na chamada abordagem estrutural, co...

Statistical properties of circulation encode relevant information about the multiscale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, such as the dependence of circulation moments upon Reynolds numbers and length scales, and the specific shape of the heavy-tailed circulation probabil...

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...

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 pr...

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...

Skewness and non-Gaussian behavior are key features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, the physical origin of the asymmetry and the form of the heavy tails remain elusive. Here we describe the emergence of such properties through an exactly solvable stochastic model with a hierarchy of multiple...

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...

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 st...

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 (MSR) 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 equat...

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 (MSR) 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 equat...

The analysis of fluid turbulence properties is traditionally carried on from the statistics of the three-dimensional velocity field increments. This approach has led to important results such as Kolmogorov's 4/5 law. Multifractal analysis, developed to characterize these statistical properties, has seen the emergence of more efficient tools through...

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 th...

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 re...

We present advances in various aspects of the theory, phenomenology and numerical analysis of homogeneous turbulence, employing a varied collection of theoretical and computational tools. We start discussing the foundations of the statistical theory of turbulence, developed primarily by Taylor in 1935 and Kolmogorov in 1941, to make the thesis acce...

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 a...

The nature of a phase transition depends dramatically on the system’s dimensionality and symmetries. In particular, the continuum phase transitions in two-dimensional systems possess an infinite dimensional symmetry group called the conformal group. Important quantities from the physical point of view, such as critical exponents and correlation func...