Generation and characterization of absolute equilibrium of compressible flows

Giorgio Krstulovic; Carlos Cartes; Marc Brachet; Enrique Tirapegui

doi:10.1142/S021812740902489X

Generation and characterization of absolute equilibrium of compressible flows

Giorgio Krstulovic^*, Carlos Cartes, Marc Brachet, Enrique Tirapegui

^*Corresponding author for this work

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

10 Scopus citations

Abstract

A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k² scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound.

Original language	English
Pages (from-to)	3445-3459
Number of pages	15
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	19
Issue number	10
DOIs	https://doi.org/10.1142/S021812740902489X
State	Published - Oct 2009
Externally published	Yes

Bibliographical note

Funding Information:
We acknowledge support from an ECOS/ CONICYT action and one of the authors (ET) is grateful to the Project ACT 15 of CONICYT, Chile. The computations were carried out at IDRIS (CNRS).

Keywords

Clebsch potentials
Compressible fluids
Relaxation
Truncated Euler equation

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10.1142/S021812740902489X

Cite this

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title = "Generation and characterization of absolute equilibrium of compressible flows",

abstract = "A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k2 scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound.",

keywords = "Clebsch potentials, Compressible fluids, Relaxation, Truncated Euler equation",

author = "Giorgio Krstulovic and Carlos Cartes and Marc Brachet and Enrique Tirapegui",

note = "Funding Information: We acknowledge support from an ECOS/ CONICYT action and one of the authors (ET) is grateful to the Project ACT 15 of CONICYT, Chile. The computations were carried out at IDRIS (CNRS).",

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T1 - Generation and characterization of absolute equilibrium of compressible flows

AU - Krstulovic, Giorgio

AU - Cartes, Carlos

AU - Brachet, Marc

AU - Tirapegui, Enrique

N1 - Funding Information: We acknowledge support from an ECOS/ CONICYT action and one of the authors (ET) is grateful to the Project ACT 15 of CONICYT, Chile. The computations were carried out at IDRIS (CNRS).

PY - 2009/10

Y1 - 2009/10

N2 - A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k2 scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound.

AB - A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k2 scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound.

KW - Clebsch potentials

KW - Compressible fluids

KW - Relaxation

KW - Truncated Euler equation

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DO - 10.1142/S021812740902489X

M3 - Article

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SN - 0218-1274

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SP - 3445

EP - 3459

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 10

ER -

Generation and characterization of absolute equilibrium of compressible flows

Abstract

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Keywords

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