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Conformal Invariance of Characteristic Lines in a Class of Hydrodynamic Models

Wacławczyk, Marta ; Grebenev, Vladimir N. ; Oberlack, Martin (2023)
Conformal Invariance of Characteristic Lines in a Class of Hydrodynamic Models.
In: Symmetry, 2020, 12 (9)
doi: 10.26083/tuprints-00015966
Article, Secondary publication, Publisher's Version

Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

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Item Type: Article
Type of entry: Secondary publication
Title: Conformal Invariance of Characteristic Lines in a Class of Hydrodynamic Models
Language: English
Date: 4 December 2023
Place of Publication: Darmstadt
Year of primary publication: 2020
Place of primary publication: Basel
Publisher: MDPI
Journal or Publication Title: Symmetry
Volume of the journal: 12
Issue Number: 9
Collation: 19 Seiten
DOI: 10.26083/tuprints-00015966
Corresponding Links:
Origin: Secondary publication DeepGreen

This paper addresses the problem of the existence of conformal invariance in a class of hydrodynamic models. For this we analyse an underlying transport equation for the one-point probability density function, subject to zero-scalar constraint. We account for the presence of non-zero viscosity and large-scale friction. It is shown analytically, that zero-scalar characteristics of this equation are invariant under conformal transformations in the presence of large-scale friction. However, the non-zero molecular diffusivity breaks the conformal group (CG). This connects our study with previous observations where CG invariance of zero-vorticity isolines of the 2D Navier–Stokes equation was analysed numerically and confirmed only for large scales in the inverse energy cascade. In this paper, an example of CG is analysed and possible interpretations of the analytical results are discussed.

Uncontrolled Keywords: conformal symmetry, Lundgren–Monin–Novikov equations, method of characteristics
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-159660
Additional Information:

This article belongs to the Special Issue Symmetry in Fluid Flow

Classification DDC: 500 Science and mathematics > 530 Physics
600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 04 Dec 2023 10:18
Last Modified: 13 Dec 2023 12:50
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/15966
PPN: 513918841
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