arXiv subjects

V. J. Valadão

Publications and source records attributed to V. J. Valadão.

9 recordsLinked to original sources

arXiv2026

Growth of small localized perturbations in Surface Quasi-Geostrophic turbulence

The butterfly effect, namely the amplification of an initially localized infinitesimal perturbation, is a fundamental hallmark of chaotic systems. While this phenomenon is well understood in low-dimensional chaotic systems, its implications become more complex in spatially extended systems characterized by multiple temporal and spatial scales, such as geophysical flows. In this Letter, we investigate the butterfly effect by examining the evolution of infinitesimal localized perturbations in a minimal model of mesoscale geophysical turbulence. We find that localized perturbations exhibit highly variable dynamics, including an initial transient regime during which perturbation energy decreases while the error spectrum shifts from the injection scale toward the system's most unstable configuration. The duration of this transient regime spans a broad range and may persist for several characteristic small-scale times, depending on the perturbation's size, its initial location, and the Reynolds number.

physics.ao-ph↗

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.

physics.flu-dyn↗

arXiv2025

Scaling and Predictability in Surface Quasi-Geostrophic Turbulence

Turbulent flows are strongly chaotic and unpredictable, with a Lyapunov exponent that increases with the Reynolds number. Here, we study the chaoticity of the Surface Quasi-geostrophic system, a two-dimensional model for geophysical flows that displays a direct cascade similar to that of three-dimensional turbulence. Using high-resolution direct numerical simulations, we investigate the dependence of the Lyapunov exponent on the Reynolds number and find an anomalous scaling exponent larger than the one predicted by dimensional arguments. We also study the finite-time fluctuation of the Lyapunov exponent by computing the Cramér function associated with its probability distribution. We find that the Cramér function attains a self-similar form at large Re.

physics.flu-dyn↗

arXiv2025

Spectrum correction in Ekman-Navier-Stokes turbulence

The presence of a linear friction drag affects significantly the dynamics of turbulent flows in two-dimensions. At small scales, it induces a correction to the slope of the energy spectrum in the range of wavenumbers corresponding to the direct enstrophy cascade. Simple arguments predict that this correction is proportional to the ratio of the friction coefficient to the characteristic deformation rate of the flow. In this work, we examine this phenomenon by means of a set of GPU-accelerated numerical simulations at high resolutions, varying both the Reynolds number and the friction coefficient. Exploiting the relation between the energy spectrum and the enstrophy flux, we obtain accurate measurements of the spectral scaling exponents. Our results show that the exponent of the spectral correction follows a universal linear law in which the friction coefficient is rescaled by the enstrophy injection rate.

physics.flu-dyn↗

arXiv2024

Circulation Statistics in Homogeneous and Isotropic Turbulence

This is the final version of a Thesis presented to the PostGrad Program in Physics of the Physics Institute of the Federal University of Rio de Janeiro (UFRJ), as a necessary requirement for the title of Ph.D. in Science (Physics). The development of the Vortex Gas Model (VGM) introduces a novel statistical framework for describing the characteristics of velocity circulation. In this model, the underlying foundations rely on the statistical attributes of two fundamental constituents. The first is a GMC field that governs intermittent behavior and the second constituent is a Gaussian Free field responsible for the partial polarization of the vortices in the gas. The model is revisited in a more sophisticated language, where volume exclusion among vortices is addressed. These additions were subsequently validated through numerical simulations of turbulent Navier-Stokes equations. This revised approach harmonizes with the multifractal characteristics exhibited by circulation statistics, offering a compelling elucidation for the phenomenon of linearization of the statistical circulation moments, observed in recent numerical simulation. In the end, a field theoretical approach, known as Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional method is carried out in the context of circulation probability density function. This approach delves into the realm of extreme circulation events, often referred to as Instantons, through two distinct methodologies: The First investigates the linear solutions and, by a renormalization group argument a time-rescaling symmetry is discussed. Secondly, a numerical strategy is implemented to tackle the nonlinear instanton equations in the axisymmetric approximation. This approach addresses the typical topology exhibited by the velocity field associated with extreme circulation events.

physics.flu-dyn↗

arXiv2024

Non-equilibrium fluctuations of the direct cascade in Surface Quasi Geostrophic turbulence

We study the temporal fluctuations of the flux of surface potential energy in Surface Quasi-Geostrophic (SQG) turbulence. By means of high-resolution, direct numerical simulations of the SQG model in the regime of forced and dissipated cascade of temperature variance, we show that the instantaneous imbalance in the energy budget originates a subleading correction to the spectrum of the turbulent cascade. Using a multiple-scale approach combined with a dimensional closure we derive a theoretical prediction for the power-law behavior of the corrections, which holds for a class of turbulent transport equations known as α-turbulence. Further, we develop and apply a method to disentangle the equilibrium and non-equilibrium contribution in the instantaneous spectra, which can be generalized to other turbulent systems.

physics.flu-dyn↗

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.

physics.flu-dyn↗

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.

physics.flu-dyn↗

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.

physics.flu-dyn↗