Next Article in Journal
Geometric Shrinkage Priors for Kählerian Signal Filters
Next Article in Special Issue
Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions
Previous Article in Journal
A Link between Nano- and Classical Thermodynamics: Dissipation Analysis (The Entropy Generation Approach in Nano-Thermodynamics)
Previous Article in Special Issue
Thermodynamic Analysis about Nucleation and Growth of Cubic Boron Nitride Crystals in the hBN-Li3N System under High Pressure and High Temperature
Open AccessArticle

Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation

Istituto dei Sistemi Complessi ISC-CNR, via Madonna del Piano 10, 50019 Sesto Fiorentino (Florence), Italy
Academic Editor: Ignazio Licata
Entropy 2015, 17(3), 1329-1346; https://doi.org/10.3390/e17031329
Received: 15 November 2014 / Revised: 3 March 2015 / Accepted: 9 March 2015 / Published: 16 March 2015
The dynamics of dissipative fluids in Eulerian variables may be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the frictionless limit of the system via a symmetric semidefinite component, encoding dissipative forces. The metriplectic algebra includes the conserved total Hamiltonian H, generating the non-dissipative part of dynamics, and the entropy S of those microscopic degrees of freedom draining energy irreversibly, which generates dissipation. This S is a Casimir invariant of the Poisson algebra to which the metriplectic algebra reduces in the frictionless limit. The role of S is as paramount as that of H, but this fact may be underestimated in the Eulerian formulation because S is not the only Casimir of the symplectic non-canonical part of the algebra. Instead, when the dynamics of the non-ideal fluid is written through the parcel variables of the Lagrangian formulation, the fact that entropy is symplectically invariant clearly appears to be related to its dependence on the microscopic degrees of freedom of the fluid, that are themselves in involution with the position and momentum of the parcel. View Full-Text
Keywords: fluid dynamics; Hamiltonian formulations; Lagrangian and Hamiltonian mechanics fluid dynamics; Hamiltonian formulations; Lagrangian and Hamiltonian mechanics
MDPI and ACS Style

Materassi, M. Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation. Entropy 2015, 17, 1329-1346.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Only visits after 24 November 2015 are recorded.
Back to TopTop