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 and Prykarpatski AK

Basic information

Original name

Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants

Authors

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

Edition

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

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10102 Applied mathematics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 2.524

Organization unit

Faculty of Science

DOI

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

UT WoS

000593678300001

Keywords in English

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

Abstract

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 and Prykarpatski AK. Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants. Entropy. Basel (Schwitzerland): MDPI AG, POSTFACH, 2020, vol. 22, No 11, 26 pp. ISSN 1099-4300. Available from: 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 and Prykarpatski AK. Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants. \textit{Entropy}. Basel (Schwitzerland): MDPI AG, POSTFACH, 2020, vol.~22, No~11, 26 pp. ISSN~1099-4300. Available from: https://dx.doi.org/10.3390/e22111241.

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