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@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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