Asymptotic series in dynamics of fluid flows: Diffusion versus bifurcations

D. Volchenkov; R. Lima

doi:10.1016/j.cnsns.2006.11.005

Asymptotic series in dynamics of fluid flows: Diffusion versus bifurcations

D. Volchenkov, R. Lima

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high order asymptotic coefficients are studied. Similarly to the models of quantum field theory, the asymptotic contributions show a factorial growth and are summated by means of Borel's procedure. The resulting corrected diffusion spectrum has a closed analytical form. The approach provides a possible ground for the optimization of existing numerical simulation algorithms and can be used for the analysis of other asymptotic series in turbulence.

Original language	English
Pages (from-to)	1329-1342
Number of pages	14
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	13
Issue number	7
DOIs	https://doi.org/10.1016/j.cnsns.2006.11.005
State	Published - Sep 2008

Keywords

Asymptotic series
Borel summation
Brownian motion
Simulation on fluid flows

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10.1016/j.cnsns.2006.11.005

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title = "Asymptotic series in dynamics of fluid flows: Diffusion versus bifurcations",

abstract = "The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high order asymptotic coefficients are studied. Similarly to the models of quantum field theory, the asymptotic contributions show a factorial growth and are summated by means of Borel's procedure. The resulting corrected diffusion spectrum has a closed analytical form. The approach provides a possible ground for the optimization of existing numerical simulation algorithms and can be used for the analysis of other asymptotic series in turbulence.",

keywords = "Asymptotic series, Borel summation, Brownian motion, Simulation on fluid flows",

author = "D. Volchenkov and R. Lima",

note = "Funding Information: One of the authors (D.V.) is grateful to the Alexander von Humboldt Foundation (Germany) and the research contract CEA/EURQTOM N 006385 for the support that he gratefully acknowledges. While preparing the paper, D.V. had benefited from the hospitality of the Zentrum fur Interdisciplinaere Forschung, Universitaet Bielefeld (Germany).",

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T2 - Diffusion versus bifurcations

AU - Volchenkov, D.

AU - Lima, R.

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N2 - The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high order asymptotic coefficients are studied. Similarly to the models of quantum field theory, the asymptotic contributions show a factorial growth and are summated by means of Borel's procedure. The resulting corrected diffusion spectrum has a closed analytical form. The approach provides a possible ground for the optimization of existing numerical simulation algorithms and can be used for the analysis of other asymptotic series in turbulence.

AB - The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high order asymptotic coefficients are studied. Similarly to the models of quantum field theory, the asymptotic contributions show a factorial growth and are summated by means of Borel's procedure. The resulting corrected diffusion spectrum has a closed analytical form. The approach provides a possible ground for the optimization of existing numerical simulation algorithms and can be used for the analysis of other asymptotic series in turbulence.

KW - Asymptotic series

KW - Borel summation

KW - Brownian motion

KW - Simulation on fluid flows

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DO - 10.1016/j.cnsns.2006.11.005

M3 - Article

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EP - 1342

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

IS - 7

ER -

Asymptotic series in dynamics of fluid flows: Diffusion versus bifurcations

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