Laboratory of Fluid Dynamics


Room 108 (first floor)

Instituto Nacional de Matemática Pura e Aplicada - IMPA

Estrada Dona Castorina 110, Rio de Janeiro 22460-320 Brazil

Tel.: +55 21 2529 5070

Fax: +55 21 2529 5075

Homepage: http://fluid.impa.br


Brazilian Chapter of InterPore

The International Society for Porous Media


How to get to IMPA

Ph.D. THESIS DEFENSE

Ph.D. Student: Ciro Sobrinho Campolina Martins

Ph.D. Advisor: Alexei A. Mailybaev

 

Thesis: Fluid Flows and Boundaries on Logarithmic Lattices

 

Abstract: Several open problems in fluid dynamics are related to the multi-scale nature of turbulence and the effects of boundary conditions. To overcome the limited resolution of direct numerical simulations, simplified toy-models are commonly employed in the study of large spatial range flows. In the construction of such models, one modifies equations of motion, preserving only certain parts believed to be important. In this thesis, we propose a different approach. Instead of simplifying equations, one introduces a simplified configuration space: we define velocity fields and boundary effects on multi-dimensional logarithmic lattices in Fourier space. Operations upon these variables are provided in a rigorous mathematical framework, so equations of motion are written in their exact original form. As a consequence, the resulting models preserve the same symmetry groups, inviscid invariants and regularity properties. The strong reduction in degrees of freedom allows computational simulations of incredibly large spatial ranges. Using the new simplified models, we address two important open problems: the finite time singularities in ideal flow and the vanishing viscosity limit in the presence of solid boundaries. We observe strong robustness of the chaotic blowup scenario in the three-dimensional incompressible Euler equations and promising results towards the investigation of potentially singular behavior close to solid boundaries.
 

Wednesday, Nov. 30, 2022 at 10:00 AM (RJ)

 

 

Pós-doutor do IMPA participa de seminário em Cartagena

 

News: https://impa.br/noticias/pos-doutor-do-impa-participa-de-seminario-em-cartagena/

 

A matemática aplicada no cálculo da trajetória de foguetes, no comportamento e evolução de tumores de mama, no resfriamento do vidro e na construção de redes neurais para desenvolvimento de inteligência artificial. São exemplos como esse, da ciência utilizada no setor produtivo e na sociedade, que Marlon López, pós-doutor no laboratório de Dinâmica dos Fluidos do IMPA, levará para o 4º Encontro Matemático do Caribe, que acontece de 29 de novembro a 2 de dezembro, em Cartagena, na Colômbia.

López apresentará a palestra “A importância da modelação matemática no desenvolvimento tecnológico” na conferência de abertura do evento. O fórum será realizado no Parque Industrial e Tecnológico Carlos Vélez Pombo. Também haverá transmissão online do encontro.

 

 

Fluid Flows and Boundaries on Logarithmic Lattices

Expositor: Ciro S. Campolina - IMPA
Qui 24 nov 2022, 13:30 - SALA 224
Seminário de Matemática Aplicada e Computacional
 

Resumo: Several open problems in fluid dynamics are related to the multi-scale nature of turbulence and the effects of boundary conditions. To overcome the limited resolution of direct numerical simulations, simplified toy-models are commonly employed in the study of large spatial range flows. In the construction of such models, one modifies equations of motion, preserving only certain parts believed to be important. In this thesis, we propose a different approach. Instead of simplifying equations, one introduces a simplified configuration space: we define velocity fields and boundary effects on multi-dimensional logarithmic lattices in Fourier space. Operations upon these variables are provided in a rigorous mathematical framework, so equations of motion are written in their exact original form. As a consequence, the resulting models preserve the same symmetry groups, inviscid invariants and regularity properties. The strong reduction in degrees of freedom allows computational simulations of incredibly large spatial ranges. Using the new simplified models, we address two important open problems: the finite time singularities in ideal flow and the vanishing viscosity limit in the presence of solid boundaries. We observe strong robustness of the chaotic blowup scenario in the three-dimensional incompressible Euler equations and promising results towards the investigation of potentially singular behavior close to solid boundaries. These are results of my PhD research under the supervision of Prof. Alexei Mailybaev.

 

Webpage: https://impa.br/seminarios

 

Ph.D. THESIS DEFENSE

Ph.D. Student: Júlia Domingues Lemos

Ph.D. Advisor: Alexei A. Mailybaev

 

Thesis: Data-based approach for time-correlated closures of turbulence models

 

Abstract: Developed turbulent motion of fluid still lacks an analytical description despite more than a century of active research. Nowadays phenomenological ideas are widely used in practical applications, such as small-scale closures for numerical simulations of turbulent flows. In the present work, we use a shell model of turbulence to construct a closure intended to have a solid theoretical background and to capture intrinsic probabilistic features of turbulence. Shell models of turbulence are dynamical deterministic systems used to model energy cascade and other key aspects of the Navier-Stokes equation. Some, such as the Sabra model, also present intermittency. We rescale the variables of the Sabra model in a way which leads to hidden symmetries and universal distributions. We then use such fine distributions to write closures, i.e., missing expressions for some of the Sabra variables. Our closures rely on approximating probability density functions using a Gaussian Mixture Model, which makes them probabilistic by nature and allows us to write time-correlated closures. We also provide a framework where other Machine Learning tools can be employed with reduced black-box aspects.

Keywords: turbulence, shell models, probabilistic closure, time-correlation, hidden symmetry.
 
 
 

 

Friday Oct. 14, 2022 10:00 AM (RJ)

 

 

Depinning asymptotics in ergodic media

Expositor: Sergey Tikhomirov - IMPA
Qui 08 set 2022, 13:30 - SALA 224 Seminário de Matemática Aplicada e Computacional
 

Resumo: We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent depending a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are satisfied in a context of weak inhomogeneity of the medium and almost balanced kinetics.

The talk is based on a joint work with A. Scheel

Webpage: https://impa.br/seminarios

 

Spontaneous stochasticity in experimental turbulence : from thermal noise to irreversibility

Expositor: Antoine Barlet - Universite Paris-Saclay & IMPA + CEA
Qui 01 set 2022, 13:30 - SALA 224 Seminário de Matemática Aplicada e Computacional
 

Resumo: This talk aims at introducing some general ideas to find experimental evidence of spontaneous stochasticity in turbulence.

Some recent theories reconsidered thermal noise when it comes to correctly modeling small scales of turbulence; noise that might also be at the origin of spontaneous stochasticity. The first part of this talk will be dedicated on introducing the experiment and discussing the use of hot-wires to try to observe those weakly energetic random fluctuations.

The study of relation between spontaneous stochasticity and irreversibility will be presented in a second part. We will be especially discussing the use of tools from differential geometry and phase transition theory to enlighten experimental data analysis.

 

Webpage: https://impa.br/seminarios

 

 

Spontaneous Stochasticity in the Kraichnan Model of Turbulence

Expositor: André Luís Peixoto Considera - IMPA
Qui 18 ago 2022, 13:30 - SALA 224
Seminário de Matemática Aplicada e Computacional
 

Resumo: In this talk we discuss the Kraichnan model of passive scalar advection, which can be used to model turbulent dispersion of particles. We give a brief introduction of the main concepts related to the model and proceed to show how the phenomenon of spontaneous stochasticity takes place in the framework of Gaussian velocity (random) fields. Possible extension to non-Gaussian (intermittent) velocity fields are also discussed.

Webpage: https://impa.br/seminarios

 

Wave-particle dynamics in hydrodynamic quantum analogues

Expositor: André Nachbin - IMPA
Qui 04 ago 2022, 13:30 - SALA 224
Seminário de Matemática Aplicada e Computacional
 

Resumo: The groundbreaking discovery by Yves Couder and Emmanuel Fort (Paris, 2005) led to many works on pilot-wave hydrodynamics. Pilot-wave hydrodynamics originates from bouncing droplets of silicon oil that can levitate over a vibrating bath of the same fluid and be self-propelled by the Faraday waves it generates. Following Couder and Fort, these walking droplets are viewed as a hydrodynamic quantum analogue (HQA) of a wave-particle system. We have deduced the first wave-droplet dynamical system which, through scientific computing, has revealed several new dynamical properties not imagined possible for a classical mechanical system. A series of new articles have originated recently from Nachbin (Chaos 2018) where it was shown for the first time that two oscillators can be correlated at a distance, without any explicit coupling between them. An overview of these recents results will be presented, including those of a recent Nature Comm. Physics paper (June 2022) where we show the cooperative tunneling of two particles.

Webpage: https://impa.br/seminarios

 

News

 

The 5th-Interpore conference of the Brazilian chapter, will be held from 1 to 2 August 2022 in a fully virtual format with scientific program focusing on advances in the research, methods, and theory of Porous Media in close connection to the topics: Green World, Smart Materials, Oil Science and Synchrotron light, Biosciences, Biorenewables, Nanotechnology.

Webpage: https://interpore2022br.ufrn.br/

 

 

Ph.D. THESIS DEFENSE

Ph.D. Student: José Manuel Escorcia Tafur

Thesis: Post-Blowup Dynamics for the Nonlinear Schrödinger Equation

José Manuel has been working during his doctoral studies under the supervision of Professor Alexei A. Mailybaev.

 

https://impa.br/noticias/pesquisando-escorcia-aprendeu-linguagem-universal-da-ciencia/

 

Monday Nov. 29, 2021 12:30 PM (RJ)

 

 

LECTURE NOTES 

of the course "An Introduction to Stochastic Differential Equations with applications to Fluid Dynamics" by Theodore Drivas and Simon Thalabard.

January-February 2019:

Mon, Wed, Fri 10-12 a.m. at room 345


Webpage: http://www.interpore2019br.lncc.br/


Presentation slides

Workshop program


06/aug, 13:00, room 228: Group meeting: talks by Ciro Campolina and Vitor Sudbrack. 


Thesis Defense of Luis Fernando Lozano: "Diffusive effects in Riemann solutions for three phase flow in porous media". 
27/07/2018 - 13:30 at room 228.


Seminar (11/07): Marco Martins Afonso (Centro de Matemática da Universidade do Porto) "Renormalized transport of inertial particles", 11:00, room 228.


Seminar (26/06): Luis Fernando Lozano Guerrero (IMPA) "Estudo do efeito de difusão (simplificada) em sistemas não estritamente hiperbólicos de leis de conservação", 13:30 at room 347.


Seminar (06/06): Carlos Galeano-Ríos ( Math. Dept., University of Bath, England) "Ratcheting pairs of droplets", 11:00 at room 333.

Lectures at IMPA by Prof. Uriel Frisch, May 11-17.


Seminar (26/03): John Bush (MIT - Dep. of Mathematics) 
"Hydrodynamic quantum analogs", 11:00 at room 228.


The paper by Prof. Mailybaev showing that light stops at exceptional points is  featured in newspapers and science news articles: NewsweekThe Independent, Daily Mail, Phys.org, ScienceAlert.
IMPA's press release (portuguese) may be read here.

Credit: pixabay


Group meeting: Hugo Saraiva, Turbulence reading course
- 20/fev, 10:30, room 224
- 06/feb, 10:30, room 224
- 30/jan, 10:30, room 224
- 23/jan, 10:30, room 224


Seminar: Vikas Krishnamurthy (UFPe), Complex analysis for compressible vortex dynamics (16/jan, 15:30, room 333)
Group meeting: Hugo Saraiva, Turbulence reading course (09/jan, 10:30, room 345)

(12/2017) Tribute to Clarice Lispector and Leopoldo Nachbin


Group meeting: Hugo Saraiva, Theory for Lattice-Boltzmann Method for two-phase flows - part 2 (07/dec, 13:30, room 333)


Group meeting: Hugo Saraiva, Theory for Lattice-Boltzmann Method for two-phase flows - part 1 (30/nov, 13:30, room 333)

(09/2017) Article about the career and life of professor Dan Marchesin, our Laboratory's Head and founder (English / Portuguese)


Videos: talks of the Workshop on Conservation Laws and Applications, celebrating the 70th birthday of Dan Marchesin

  70th birthday of Dan Marchesin


 Interview: O Globo (05/2017)

Seminar: Wanderson Lambert, Teoria matemática de fluxo bifásico em meios porosos com diversos componentes químicos (24/mar, 10:30, room 236)

Group meeting: Hugo Saraiva, Entropy (24/mar, 13:30, room 236)

Group meeting: Hugo Saraiva, Boltzmann equation (9/mar, 13:30, room 345)



 Interview for Galileu (03/2017).


Videos: IMPA-Bath Workshop in Mathematics

 


 Interview for Globo (02/2017)


Videos: Workshop on Turbulent Dissipation, Mixing and Predictability. January 9 - 13, 2017, IPAM, Los Angeles


Videos: 2nd IMPA-InterPore Conference on Porous Media