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, roč. 22, č. 11, 26 s. ISSN 1099-4300. doi:10.3390/e22111241. 2020.
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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
Originální jazyk angličtina
Typ výsledku Článek v odborném periodiku
Obor 10102 Applied mathematics
Stát vydavatele Švýcarsko
Utajení není předmětem státního či obchodního tajemství
WWW 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
Změnil Změnila: Mgr. Marie Šípková, DiS., učo 437722. Změněno: 15. 2. 2024 09:28.
Anotace
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.
VytisknoutZobrazeno: 28. 3. 2024 10:58