Magnetic fields from multiplicative chaos

Durrive, Jean-Baptiste; Lesaffre, Pierre; Ferrière, K.

doi:10.1093/mnras/staa1514

Cited by 12 publications

(21 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A tarefa de demonstrar exatamente sua multifractalidade ou de construir outro objeto similar exatamente multifractal permanece aberta, e esforços continuam a ser realizados nessa direção [190]. Ademais, em um trabalho deste ano, desdobramentos no cenário consideravelmente mais complexo da magnetohidrodinâmica, em que campos magnéticos estão acoplados ao fluido, foram propostos com o intuito de modelar a dinâmica de meios astrofísicos [191].…”

Section: Modelagem Estocásticaunclassified

A física estatística da turbulência

Moriconi

Pereira

2021

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

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, como o desafio de compreender, a partir da dinâmica de tubos de vorticidade, o transporte de energia das grandes para as pequenas escalas do escoamento, no limite singular de viscosidade nula. Propriedades estatísticas da cascata de energia, como o fenômeno da intermitência, são modeladas por meio de narrativas aparentemente diversas, associadas a processos estocásticos multiplicativos e, alternativamente, à formulação multifractal do espectro de singularidades do campo de velocidade turbulento. A síntese, fundamentação de primeiros princípios e integração dessas duas visões de modelagem à abordagem estrutural forma o corpo essencial das dificuldades teóricas atuais da turbulência.

show abstract

Section: Modelagem Estocásticaunclassified

A física estatística da turbulência

Moriconi

Pereira

2021

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

show abstract

“…The model we consider was first introduced in Chevillard et al (2010) in the hydrodynamical case, and was later generalized to MHD in Durrive et al (2020). Here we use the notations from this more recent paper.…”

Section: The Bxc Modelmentioning

confidence: 99%

“…a concise, yet fairly realistic, and numerically very efficient) analytical model for incompressible hydrodynamical turbulence. This model was later extended to MHD in Durrive et al (2020) in the incompressible limit, soon after which compressibility effects were also considered in Durrive et al (2021). In Durrive et al (2020) the model was dubbed 'Magnetic fields from multiplicative chaos', because the mathematical concept underlying this construction is called 'multiplicative chaos' in the mathematics literature, a concept first introduced by Kahane (1985).…”

Section: Introductionmentioning

confidence: 99%

“…This model was later extended to MHD in Durrive et al (2020) in the incompressible limit, soon after which compressibility effects were also considered in Durrive et al (2021). In Durrive et al (2020) the model was dubbed 'Magnetic fields from multiplicative chaos', because the mathematical concept underlying this construction is called 'multiplicative chaos' in the mathematics literature, a concept first introduced by Kahane (1985). Hence, for convenience we will refer to this model as the 'BxC model', standing for 'Magnetic fields from multiplicative chaos'.…”

Section: Introductionmentioning

confidence: 99%

“…We will provide in section 2 a brief introduction to the BxC model, but the bottom line is that it is an analytical model for three-dimensional MHD turbulence which is parametric, in the sense that it contains a dozen of free (physically motivated) parameters. In Chevillard et al (2010Chevillard et al ( , 2011Chevillard et al ( , 2012Chevillard et al ( , 2013; Chevillard (2015); Pereira et al (2016Pereira et al ( , 2018 the incompressible velocity field in this model has already been confronted to both direct numerical simulations and laboratory experiments data, with an excellent agreement (see for example section 3.4 of Durrive et al 2020, for a brief review), but there is no systematic study of this model so far.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A method to statistically characterize turbulent data with physically motivated parameters, illustrated on a centroid velocity map

Durrive,

Lesaffre,

Ghosh

et al. 2021

Preprint

View full text Add to dashboard Cite

We investigate the potential of a recently proposed model for 3D compressible MHD turbulence (Chevillard et al. 2010;Durrive et al. 2021) to be used as a tool to characterize statistically 2D and 3D turbulent data. This model is parametrized by a dozen of free (intuitive, physically motivated) parameters, which control the statistics of the fields (density, velocity and magnetic fields). The present study is a proof of concept study: (i) we restrict ourselves to the incompressible hydrodynamical part of the model, (ii) we consider as data centroid velocity maps, and (iii) we let only three of the free parameters vary (namely the correlation length, the Hurst parameter and the intermittency parameter). Within this framework, we demonstrate that, given a centroid velocity map, we can find in an automated manner (i.e. by a Markov Chain Monte Carlo analysis) values of the parameters such that the model resembles the given map, i.e. which reproduces its statistics fairly well. Hence, thanks to this procedure, one may characterize statistically, and thus compare, various turbulent data. In other words, we show how this model may be used as a metric to compare observational or simulated data sets. In addition, because this model is numerically particularly fast (nearly 500 times faster than the numerical simulation we use to generate our reference data) it may be used as a surrogate model. Finally, by this process we also initiate the first systematic exploration of the parameter space of this model. Doing so, we show how the parameters impact the visual and the statistical properties of centroid velocity maps, and exhibit the correlations between the various parameters, providing new insight into the model.

show abstract

Probing the nature of dissipation in compressible MHD turbulence

Richard

Lesaffre

Falgarone

et al. 2022

A&A

Self Cite

View full text Add to dashboard Cite

Context. An essential facet of turbulence is the space-time intermittency of the cascade of energy that leads to coherent structures of high dissipation. Aims. In this work, we aim to systematically investigate the physical nature of the intense dissipation regions in decaying isothermal magnetohydrodynamical (MHD) turbulence. Methods. We probed the turbulent dissipation with grid-based simulations of compressible isothermal decaying MHD turbulence. We took unprecedented care in resolving and controlling dissipation: we designed methods to locally recover the dissipation due to the numerical scheme. We locally investigated the geometry of the gradients of the fluid state variables. We developed a method to assess the physical nature of the largest gradients in simulations and to estimate their travelling velocity. Finally, we investigated their statistics.Results. We find that intense dissipation regions mainly correspond to sheets; locally, density, velocity, and magnetic fields vary primarily in one direction. We identify these highly dissipative regions as fast and slow shocks or Alfvén discontinuities (Parker sheets or rotational discontinuities). On these structures, we find the main deviation from a 1D planar steady-state is mass loss in the plane of the structure. We investigated the effect of initial conditions, which yield different imprints at an early time on the relative distributions among these four categories. However, these differences fade out after about one turnover time, at which point they become dominated by weakly compressible Alfvén discontinuities. We show that the magnetic Prandtl number has little influence on the statistics of these discontinuities, but it controls the ohmic versus viscous heating rates within them. Finally, we find that the entrance characteristics of the structures (such as entrance velocity and magnetic pressure) are strongly correlated. Conclusions. These new methods allow us to consider developed compressible turbulence as a statistical collection of intense dissipation structures. This can be used to post-process 3D turbulence with detailed 1D models apt for comparison with observations. It could also be useful as a framework to formulate new dynamical properties of turbulence.

show abstract

Magnetic fields from multiplicative chaos

Cited by 12 publications

References 59 publications

A física estatística da turbulência

A física estatística da turbulência

A method to statistically characterize turbulent data with physically motivated parameters, illustrated on a centroid velocity map

Probing the nature of dissipation in compressible MHD turbulence

Contact Info

Product

Resources

About