<  Back to the Polytechnique Montréal portal

Lifts of symmetric tensors: Fluids, plasma, and grad hierarchy

Oğul Esen, Miroslav Grmela, Hasan Gümral and Michal Pavelka

Article (2019)

Open Acess document in PolyPublie and at official publisher
Open Access to the full text of this document
Published Version
Terms of Use: Creative Commons Attribution
Download (369kB)
Show abstract
Hide abstract


Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler's fluid and the Vlasov's plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on tau*tau*Q) of (both compressible and incompressible) Euler's fluid and Vlasov's plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

Uncontrolled Keywords

diffeomorphisms group; cotangent lift; vertical representative; fluids; kinetic theory; entropy; continuum-mechanics; poisson brackets; complex fluids; thermodynamics; equations; dynamics; formulation; geometry; moments; systems

Subjects: 1800 Chemical engineering > 1800 Chemical engineering
Department: Department of Chemical Engineering
Funders: CRSNG/NSERC, Czech Science Foundation, Charles University Research Program
Grant number: 3100319, 3100735, 17-15498Y, UNCE/SCI/023
PolyPublie URL: https://publications.polymtl.ca/4857/
Journal Title: Entropy (vol. 21, no. 9)
Publisher: MDPI
DOI: 10.3390/e21090907
Official URL: https://doi.org/10.3390/e21090907
Date Deposited: 16 Aug 2021 14:26
Last Modified: 19 May 2023 00:08
Cite in APA 7: Esen, O., Grmela, M., Gümral, H., & Pavelka, M. (2019). Lifts of symmetric tensors: Fluids, plasma, and grad hierarchy. Entropy, 21(9). https://doi.org/10.3390/e21090907


Total downloads

Downloads per month in the last year

Origin of downloads


Repository Staff Only

View Item View Item