Geometric aspects of the isentropic liquid dynamics and vorticity invariants
Authors:
- Alexander A. Balinsky,
- Denis Blackmore,
- Radosław Kycia,
- Anatolij K. Prykarpatski
Abstract
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.
- Record ID
- CUT8d01eced816f43508ff7391465149720
- Publication categories
- ;
- Author
- Other language title versions
- Geometric aspects of the isentropic liquid dynamics and vorticity invariants
- Journal series
- Entropy, ISSN , e-ISSN 1099-4300, Monthly
- Issue year
- 2020
- Vol
- 22
- No
- 11
- Pages
- [1-26]
- Article number
- 1241
- Other elements of collation
- Bibliografia (na s.) - 24-26; Bibliografia (liczba pozycji) - 51; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 22, Iss. 11, Spec. Iss.
- Substantive notes
- Special Issue: Review Papers for Entropy
- Keywords in English
- liquid flow, hydrodynamic Euler equations, diffeomorphism group, Lie-Poisson structure, isentropic hydrodynamic invariants, vortex invariants, charged liquid fluid dynamics, symmetry reduction
- DOI
- DOI:10.3390/e22111241 Opening in a new tab
- URL
- https://www.mdpi.com/1099-4300/22/11/1241 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 100
- Publication indicators
- = 2
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT8d01eced816f43508ff7391465149720/
- URN
urn:pkr-prod:CUT8d01eced816f43508ff7391465149720
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.