Eddy-viscous modeling and the topology of extreme circulation events in three-dimensional turbulence

Apolinário, Gabriel B.; Moriconi, L.; Pereira, R. M.; Valadão, V. J.

doi:10.1016/j.physleta.2022.128360

Cited by 5 publications

(2 citation statements)

References 78 publications

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“…Unfortunately, the perturbative approach followed in this work was doomed to fail as instantons are nonperturbative objects by nature. The nonperturbative instanton analysis of intermittency in fluid turbulence was initiated by Falkovich et al in [25], but many questions are still open [26,27]. Since then, advances and new applications of the instanton approach in stochastic field theories have been made.…”

Section: Introductionmentioning

confidence: 99%

Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit

Mounaix

2023

J. Phys. A: Math. Theor.

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We study the tail of $p(U)$, the probability distribution of $U=\vert\psi(0,L)\vert^2$, for $\ln U\gg 1$, $\psi(x,z)$ being the solution to $\partial_z\psi -\frac{i}{2m}\nabla_{\perp}^2 \psi =g\vert S\vert^2\, \psi$, where $S(x,z)$ is a complex Gaussian random field, $z$ and $x$ respectively are the axial and transverse coordinates, with $0\le z\le L$, and both $m\ne 0$ and $g>0$ are real parameters. We perform the first instanton analysis of the corresponding Martin-Siggia-Rose action, from which it is found that the realizations of $S$ concentrate onto long filamentary instantons, as $\ln U\to +\infty$. The tail of $p(U)$ is deduced from the statistics of the instantons. The value of $g$ above which $\langle U\rangle$ diverges coincides with the one obtained by the completely different approach developed in Mounaix et al. 2006 {\it Commun. Math. Phys.} {\bf 264}~741. Numerical simulations clearly show a statistical bias of $S$ towards the instanton for the largest sampled values of $\ln U$. The high maxima --- or `hot spots' --- of $\vert S(x,z)\vert^2$ for the biased realizations of $S$ tend to cluster in the instanton region.

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Section: Introductionmentioning

confidence: 99%

Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit

Mounaix

2023

J. Phys. A: Math. Theor.

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“…In the turbulence or transitional context, instantons are taken, respectively, as extreme events or flow configurations that dominate the probability measures in the weak coupling limit. They have been successfully applied to a number of fluid dynamic problems, as in geophysical models, homogeneous turbulence and the laminar-turbulent transition in shear flows [15][16][17].…”

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confidence: 99%

Stochastic Model of Organizational State Transitions in a Turbulent Pipe Flow

Jäckel¹,

Magacho²,

Owolabi³

et al. 2023

Preprint

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Scalable methods for computing sharp extreme event probabilities in infinite-dimensional stochastic systems

Schorlepp,

Tong,

Grafke

et al. 2023

Stat Comput

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We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their efficiency does not degrade upon temporal and possibly spatial refinement. For that purpose, we extend algorithms based on the Laplace method for estimating the probability of an extreme event to infinite dimensional path space. The method estimates the limiting exponential scaling using a single realization of the random variable, the large deviation minimizer. Finding this minimizer amounts to solving an optimization problem governed by a differential equation. The probability estimate becomes sharp when it additionally includes prefactor information, which necessitates computing the determinant of a second derivative operator to evaluate a Gaussian integral around the minimizer. We present an approach in infinite dimensions based on Fredholm determinants, and develop numerical algorithms to compute these determinants efficiently for the high-dimensional systems that arise upon discretization. We also give an interpretation of this approach using Gaussian process covariances and transition tubes. An example model problem, for which we provide an open-source python implementation, is used throughout the paper to illustrate all methods discussed. To study the performance of the methods, we consider examples of stochastic differential and stochastic partial differential equations, including the randomly forced incompressible three-dimensional Navier–Stokes equations.

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Eddy-viscous modeling and the topology of extreme circulation events in three-dimensional turbulence

Cited by 5 publications

References 78 publications

Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit

Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit

Stochastic Model of Organizational State Transitions in a Turbulent Pipe Flow

Scalable methods for computing sharp extreme event probabilities in infinite-dimensional stochastic systems

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