Geometric Aspects of the Isentropic Liquid Dynamics and
Vorticity Invariants

J 2020

Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants

AA, Balinsky, Blackmore D, Radoslaw Antoni KYCIA a Prykarpatski AK

Základní údaje

Originální název

Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants

Autoři

AA, Balinsky, Blackmore D, Radoslaw Antoni KYCIA a Prykarpatski AK

Vydání

Entropy, Basel (Schwitzerland), MDPI AG, POSTFACH, 2020, 1099-4300

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10102 Applied mathematics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 2.524

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.3390/e22111241

UT WoS

000593678300001

Klíčová slova anglicky

liquid flow; hydrodynamic Euler equations; diffeomorphism group; Lie-Poisson structure; isentropic hydrodynamic invariants; vortex invariants; charged liquid fluid dynamics; symmetry reduction

Štítky

RIV ne

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 15. 2. 2024 09:28, Mgr. Marie Šípková, DiS.

Anotace

V originále

We review a modern differential geometric description of fluid isentropic motion and features of it including diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. We analyze the adiabatic liquid dynamics, within which, following the general approach, the nature of the related Poissonian structure on the fluid motion phase space as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product are explained in detail. We also present a modification of the Hamiltonian analysis in case of a flow governed by isothermal liquid dynamics. We study the differential-geometric structure of isentropic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and related invariant theory. In particular, we construct an infinite hierarchy of different kinds of integral magneto-hydrodynamic invariants, generalizing those previously constructed in the literature, and analyzing their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, and some generalizations of the canonical Lie-Poisson type bracket is presented.

Citovat

AA, Balinsky, Blackmore D, Radoslaw Antoni KYCIA a Prykarpatski AK. Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants. Entropy. Basel (Schwitzerland): MDPI AG, POSTFACH, 2020, roč. 22, č. 11, 26 s. ISSN 1099-4300. Dostupné z: https://dx.doi.org/10.3390/e22111241.

@article{1734160,
   author = {AA, Balinsky and D, Blackmore and Kycia, Radoslaw Antoni and AK, Prykarpatski},
   article_location = {Basel (Schwitzerland)},
   article_number = {11},
   doi = {http://dx.doi.org/10.3390/e22111241},
   keywords = {liquid flow; hydrodynamic Euler equations; diffeomorphism group; Lie-Poisson structure; isentropic hydrodynamic invariants; vortex invariants; charged liquid fluid dynamics; symmetry reduction},
   language = {eng},
   issn = {1099-4300},
   journal = {Entropy},
   note = {Žádný z autorů nemá afiliaci k MU.},
   title = {Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants},
   url = {https://doi.org/10.3390/e22111241},
   volume = {22},
   year = {2020}
}

TY  - JOUR
ID  - 1734160
AU  - AA, Balinsky - D, Blackmore - Kycia, Radoslaw Antoni - AK, Prykarpatski
PY  - 2020
TI  - Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants
JF  - Entropy
VL  - 22
IS  - 11
PB  - MDPI AG, POSTFACH
SN  - 10994300
N1  - Žádný z autorů nemá afiliaci k MU.
KW  - liquid flow
KW  - hydrodynamic Euler equations
KW  - diffeomorphism group
KW  - Lie-Poisson structure
KW  - isentropic hydrodynamic invariants
KW  - vortex invariants
KW  - charged liquid fluid dynamics
KW  - symmetry reduction
UR  - https://doi.org/10.3390/e22111241
N2  - We review a modern differential geometric description of fluid isentropic motion and features of it including diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. We analyze the adiabatic liquid dynamics, within which, following the general approach, the nature of the related Poissonian structure on the fluid motion phase space as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product are explained in detail. We also present a modification of the Hamiltonian analysis in case of a flow governed by isothermal liquid dynamics. We study the differential-geometric structure of isentropic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and related invariant theory. In particular, we construct an infinite hierarchy of different kinds of integral magneto-hydrodynamic invariants, generalizing those previously constructed in the literature, and analyzing their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, and some generalizations of the canonical Lie-Poisson type bracket is presented.
ER  -

AA, Balinsky, Blackmore D, Radoslaw Antoni KYCIA a Prykarpatski AK. Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants. \textit{Entropy}. Basel (Schwitzerland): MDPI AG, POSTFACH, 2020, roč.~22, č.~11, 26 s. ISSN~1099-4300. Dostupné z: https://dx.doi.org/10.3390/e22111241.

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