Mathematics of Multiscale Modeling

Room: Auditório 1 | Type: ATIVIDADES_SOCIAIS

Multiscale modeling for particle agglomeration in turbulent flows

CFD simulations of dispersed two-phase flows in practical industrial/environmental cases often rely on hybrid methods like Euler-Lagrange approaches. Yet, when dealing with the simulation of particle agglomeration, a number of additional difficulties arise in such context. In fact, particle agglomeration involves the coupling between physical phenomena occurring at various scales (e.g.interparticle adhesion at the sub-micrometer range and particle transport by a fluid over meter-sized distances). This calls for adequate methods that allow to properly account for these phenomena. This study will illustrate the various approaches that can be used to simulate particle agglomeration. In particular, we focus on hybrid Euler-Lagrange simulations and we highlight the requirements needed when relying on approaches based on mean-field statistical collision models for large-scale simulations (especially the implications in terms of physical assumptions and algorithmic precision).

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Stationary measures for partially-damped Euler-like SDE

Motivated by Kolmogorovs 1941 theory of 3D turbulence, where anomalous dissipation and the energy cascade imply a strong dynamical instability of lowmode fluid configurations, we examine a class of partially-damped bilinear SDE on , restricting the vector fields to an "Euler-like" class with properties shared by Galerkin truncations of the Euler nonlinearity, including preservation of both Euclidean spheres and Liouville measure. A priori, trajectories may linger near the undamped subspace, allowing external driving to push the system to infinity, which would be incompatible with the existence of a stationary measure for the SDE. Instability of the undamped space in this finite-dimensional setting, and the accompanied existence of a stationary measure, serve as a proxy for the dynamical instability of low-mode fluids in turbulent 3D fluids. We establish existence of stationary measures for generic systems drawn from this Euler-like class when the number of undamped modes is not too high. Joint work with Jacob Bedrossian, Kyle Liss and Keagan Callis.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Poster Flash Talks

Adhara Batista Guimarães Carvalho - Métodos Hamiltonianos Para Fluidos e Simulações que Preservam essa Estrutura
André Freitas - On the importance of stochasticity in closures of turbulence
Erika Paola Ortiz Bernal - Spontaneous Stochasticity in Fluctuating Hydrodynamics on Logarithmic Lattices
Henrique Carrano Branco Bastos - Renormalization Group Analysis of Noise Propagation on a Fractal Lattice
Mirian Andrea Geronimo Aparicio - Stochastic population dynamics: a numerical approach using SPICT in R
Raysa Gomes Dos Santos - Droplet dynamics and rheology of nondilute ferrofluid emulsions in simple shear
Wandrille Ruffenach - Spontaneous Stochasticity of the Armstrong-Vicol passive scalar

Room: Auditório 1 | Type: PALESTRA_CONTRIBUIDA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Overview on the predictability of SQG turbulence

The Surface Quasi-Geostrophic (SQG) equation is a two-dimensional model for rapidly rotating and stably stratified fluids and represents a fundamental framework for the study of geophysical turbulence. Despite its reduced dimensionality, SQG turbulence exhibits a direct energy cascade with statistical and dynamical properties that are closer to those of three-dimensional turbulence than to classical two-dimensional flows. This makes it a valuable model to investigate fundamental aspects of multiscale turbulent dynamics. This talk provides an overview of recent results on the statistical and predictability properties of forced-dissipative SQG turbulence. General features of the direct cascade, including intermittency and nonequilibrium behavior, are discussed, together with predictability properties in both Eulerian and Lagrangian frameworks. Particular attention is devoted to the evolution of small perturbations across scales and to their possible impact on large-scale flow organization, in connection with the so-called real butterfly effect. The talk concludes by outlining open problems and future research directions, including data-driven approaches to model small-scale and subgrid turbulent dynamics.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Rotation, alignment and clustering of inertial fibers in turbulence

The dynamics of non-spherical particles in turbulence are governed by the interplay between inertia and orientation-dependent hydrodynamic forces. We investigate rigid fibers dynamics by bridging two asymptotic descriptions: the small-size limit described by Jefferys equation, and the finite-length limit captured by slender-body theory. This framework enables systematic variation of aspect ratio, fiber length, and Stokes number. Using direct numerical simulations, we characterize rotational dynamics, including tumbling and rotation rates, and compare our results with available experimental and numerical studies. We further examine preferential alignment and small-scale clustering. At low Stokes numbers, fibers tend to align with the most unstable direction associated to the attractor towards which they converge and exhibit strong clustering consistent with convergence onto a fractal attractor. As the Stokes number increases, clustering is progressively reduced, with the attractor dimension approaching that of a uniform distribution, consistent with the expected behavior of inertial particles and the caustics mechanism.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

The Statistical Structure of Turbulent Vortices

Thin vortex tubes, with core sizes within the dissipation range, abound in homogeneous and isotropic turbulence (HIT). They can be depicted as the ``elementary particles" of HIT. Their intersections with an arbitrary plane define, as a mathematical construct, a dilute gas of localized and intermittently distributed two-dimensional vortex spots. While their density fluctuations are described by a field-theoretical extension of log-normal single-point statistics, known as Gaussian multiplicative chaos, they carry circulations that are Gaussian-correlated throughout the inertial range. In this talk, we discuss -- backed by strong numerical evidence -- that such small-scale vortex structures are composite objects, which couple, as a surprising phenomenological result, their circulation field to the short-distance properties of their spatial-distribution fluctuations.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Intermittency in stochastic Volterra models and Markovian approximations

In this talk, we investigate models of intermittency in Lagrangian turbulence based on stochastic Volterra dynamics. These models are formulated as integrated stochastic Volterra processes driven by kernels with a small Hurst parameter H<1/2, leading to rough temporal behaviour, strongly correlated at small scales. In the limit as H tends to zero, the corresponding log-correlated structure yields Gaussian multiplicative chaos, giving rise to multifractal scaling properties. Within a pathdependent PDE framework, we analyse numerical approximations based on quadrature rules, which provide finite-dimensional Markovian representations of the underlying non-Markovian dynamics. We establish convergence rates for these approximations, supported by numerical experiments, and we discuss how these approximation capture the multifractal features responsible for intermittency. This is a joint work with Paul Maurer and Bernard Eisvogel.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Guided Generative Models for Turbulence

We present a stochastic method for generating and reconstructing complex Eulerian and Lagrangian turbulent signals. Our approach makes use of generative Diusion Models, a recently proposed data-driven machine learning technique. We show applications to data augmentation and data assimilation for 3D tracers in Turbulence, 2D trajectories from NOAAs Global Drifter Program and extensions to the case of Eulerian multiphase bubbly flows. Supremacy against linear decomposition and Gaussian Regression Processes is analyzed in terms of statistical and point-wise metrics concerning non-Gaussian components and multi-scale properties. Preliminary results concerning generalizability and model collapse will also be discussed, as well as a personal point of view on long term goals and potentialities of black-box data-driven approaches for turbulence.

Room: Auditório 1 | Type: PALESTRA_CONTRIBUIDA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

A stochastic collisional picture of the Wave Kinetic Equation

TBA

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Extreme dissipation in particle pair dynamics at subdiffusive scales

Understanding how turbulence transports material is a key problem in geophysical flows. While pair dispersion is well characterized in the classical ballistic, superdiffusive, and diffusive regimes, much less is known about subdiffusive scales. Here, we study particle pair dispersion in turbulent flows focusing on this regime, where separation grows slower than classical predictions. Using Lagrangian analysis, we show that the dynamics is dominated by rare, intense dissipation events. These events split particle pairs into distinct subsets with markedly different dispersion behaviors. Our results indicate that subdiffusive dispersion is strongly controlled by intermittency and cannot be described by universal scaling laws. This has important implications for modeling transport and
mixing in realistic flows.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Universality of spontaneous stochasticity in the inviscid limit of turbulence

Turbulent fluid flows are described by the Navier-Stokes equations, whose inviscid limit formally leads to the Euler equations. While viscosity tends to zero, solutions may develop increasingly fine structures, raising fundamental questions about predictability and uniqueness. The evolution of infinitesimal perturbations in statistically stationary turbulent flows is analyzed by direct numerical simulations. Small errors do not remain confined to small scales: instead, they propagate toward large scales through an inertial mechanism analogous to Richardson dispersion. This growth appears to be independent of the details of energy injection, suggesting a universal phenomenon governed by the turbulent cascade itself. Such intrinsic and possibly universal spontaneous stochasticity in statistically stationary turbulence may provide a dynamical perspective of the potential non-uniqueness of weak Euler solutions in the inviscid limit, and raises the question of whether a statistical selection principle for physically relevant solutions may emerge.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

"A cheat code to Feigenbaum-Mailybaev RG” From shell models to all systems ?

We develop a bottom-up approach to constructing an abstract renormalization-group formalism aimed at treating general equivariant dynamical systems. The approach is inspired by A. Mailybaev’s Feigenbaum-type RG theory for shell models, but reformulates the underlying mechanism at a structural level. It clarifies how RG acts on regularized dynamics, how inviscid behavior is selected, and how the construction extends to nonlinear scale maps. This nonlinear viewpoint gives a natural RG formulation of finite-dimensional singularity regularizations. We conclude with a discussion of spontaneous stochasticity, both in general mathematical terms and within the RG/Perron–Frobenius framework.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

EM estimator for the drift parameter of a nonlinear McKean Vlasov diffusion

In this article, we address the problem of estimating a forcing parameter in a stochastic differential equation inspired by a model for turbulent kinetic energy. The stochastic differential equation analyzed is of the nonlinear McKeanVlasov type, with the drift depending on a power of the expected value of the solution, making the equation nonlinear also in the algebraic sense. We propose an estimation algorithm of the ExpectationMaximization type and show the consistency of the method. We illustrate our findings with numerical experiments.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Perturbative anomalous exponents from Kolmogorov multipliers

We introduce a perturbative framework for anomalous scaling in turbulent transport based on multiplier statistics, rather than zero-mode calculations. We illustrate the approach using a shell model combining deterministic and Kraichnanlike stochastic components. The problem is reduced to the analysis of a stationary Fokker--Planck equation for Kolmogorov multipliers, defined as ratios of successive scalar amplitudes. Its solution yields the invariant measure through a perturbative expansion around a Gaussian distribution. Using the resulting multiplier statistics, we compute explicit anomalous scaling exponents for structure functions of arbitrary order, including odd, even, and non-integer moments. More broadly, the results suggest that multiplier statistics provide a viable route for computing anomalous exponents in turbulent transport, complementing recent hiddensymmetry approaches while circumventing the limitations of zero-mode methods based on a closed Hopf hierarchy. This is a joint work with Simon Thalabard.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Measuring turbulence intermittency through hidden symmetry

Statistical hidden symmetries (HS) arise in the infinite-Reynolds-number limit of the NavierStokes (NS) equations when formulated in a quasi-Lagrangian, dynamically rescaled frame. However, their observation in direct numerical simulations of the standard NS equations is limited by finite-Reynolds-number effects, which breaks scale invariance. Assuming inertial-range universality, we argue that the detailed form of dissipation is subdominant for inertial-scale statistics. This motivates the use of the NavierStokesSmagorinsky (NSS) equations, where molecular viscosity is replaced by a dynamical, time-scale- and Galilean-invariant eddy viscosity. By comparing NS and NSS simulations, we obtain clear evidence for the predicted HS. We further characterize intermittency through anomalous scaling exponents and velocity structure-function statistics, highlighting deviations from Kolmogorovs 1941 theory. The hidden symmetries are found to persist robustly across resolutions within the NSS framework.This allows to use the corresponding averages in real flows as quantitative markers of isotropy by measuring their deviation from the identities.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Lattice Boltzmann modeling of dispersed multiphase flows in scale-forming environments

Simulating dispersed multiphase flows in scale-prone systems is numerically challenging. In this work, we use mesoscopic methods to model particle-laden flows and calcium carbonate (limescale) formation across a range of Reynolds numbers. The main difficulty arises when fouling layers grow: the flow physics and deposition processes interact in ways that are computationally expensive to resolve fully. Particle properties such as size, shape, density, and chemistry all affect the hydrodynamics and scaling behavior. Because no single model can capture every detail, we focus on simplified but physically meaningful descriptions. Our core strategy couples two elements: a phase-field model for moving interfaces, and an EulerianEulerian framework for transporting particles anddissolved ions. To solve the resulting equations, we design a numerical scheme based on a hybrid lattice-Boltzmann method (LBM). In particular, our LBM implementations rely on the simplified single-step formulation, which offers a favorable balance between accuracy and computational cost. Whenever possible, we validate our simulations against experiments. For model calibration, we rely on data assimilation combined with Bayesian inference. Looking ahead, we also discuss alternative EulerianLagrangian approaches based on smoothed particle hydrodynamics (SPH).

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Physics-Constrained Diffusion Model for Synthesis of 3D Turbulent Data

Synthesizing fully developed three-dimensional turbulent velocity fields remains a longstanding problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality, multiscale rough fluctuations and strong intermittency, together with exact physical constraints such as incompressibility and zero-mean momentum. In this talk we discuss a physics-constrained diffusion model (PCDM) in which a-priori constraints are incorporated directly into the generative dynamics. Using rotating turbulence as a stringent benchmark, we show that the proposed framework enables stable and statistically faithful synthesis of inertial-range three-dimensional turbulent velocity fields at medium resolution, accurately reproducing anisotropic energy spectra, intermittency statistics, and physical constraints. By contrast, standard denoising diffusion probabilistic models without such constraints exhibit multiscale statistical deviations, violations of physical consistency, and substantially slower training convergence. These findings point to broader implications for generative modeling of high-dimensional complex systems under physical constraints.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Stochastic integrals of motion and quantitative markers of statistical isotropy in turbulent flows

We present a fundamental mathematical result concerning the properties of the rotation group. For a random isotropically distributed second-rank tensor A (i.e. the one with a probability measure invariant under rotations) we demonstrate the existence of exact identities involving mathematical expectations of ATA minors. The identities represent general geometric properties of the rotation group and do not depend on the specific statistics of A. We provide several applications of this result within turbulence theory. First, a set of exact Lagrangian stochastic integrals of motion that describe the evolution of material surfaces and lines transported by an isotropic stochastic flow is found. The expression for the integrals is independent of the boundary conditions and external large-scale forces that generate the isotropic flow. Even nonlinear feedback from a transported field does not disturb the conservation. Based on this, we derive that the dynamics of ideal fluid obeys an exact conservation law for the vorticity statistics. Second, we propose a method for analyzing the statistical Eulerian properties of turbulence. We consider a tensor functionally dependent on the velocity field (e.g., the velocity gradient tensor). In an isotropic flow the identities for mathematical expectations of ATA minors are to hold. This allows to use the corresponding averages in real flows as quantitative markers of isotropy by measuring their deviation from the identities.

Room: Auditório 1 | Type: PALESTRA_PLENARIA

Room: SEM_SALA | Type: ATIVIDADES_SOCIAIS

Butterfly effect in Surface Quasi-Geostrophic flows

I will investigate chaoticity and predictability in the Surface
Quasi-Geostrophic (SQG) equation, a fundamental model for mesoscale
geophysical flows.
In particular, I will discuss how the Lyapunov exponent depends on the
Reynolds number and examine the role of intermittency. I will also analyze
the evolution of localized perturbations and their implications for flow
predictability.

Room: Auditório 1 | Type: PALESTRA_PLENARIA