Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

Morrison, Philip J.; Updike, Michael H.

doi:10.1103/physreve.109.045202

Phys. Rev. E

2024

DOI: 10.1103/physreve.109.045202

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Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

Philip J. Morrison,

Michael H. Updike

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Cited by 4 publications

References 59 publications

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Noether’s theorems and conservation laws in magnetohydrodynamics and Chew–Goldberger–Low plasmas

Webb,

Anco,

Meleshko

et al. 2024

Rev. Mod. Plasma Phys.

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The ideal magnetohydrodynamic (MHD) equations and the ideal Chew–Goldberger–Low (CGL) plasma equations are studied using Lagrangian field theory methods. Action principles for the equations are developed and used to obtain conservation laws using Noether’s theorems. The Galilean group admitted by the equations leads to (i) energy, (ii) momentum, (iii) center of mass, and (iv) angular momentum conservation laws corresponding to the time translation, space translation, Galilean boosts, and rotational symmetries, respectively. The cross-helicity conservation law is a consequence of a fluid relabeling symmetry, and is local or non-local depending on whether the entropy gradient ($$\nabla S$$ ∇ S ) is perpendicular to the magnetic field induction $$\textbf{B}$$ B or otherwise. The point Lie symmetries of the MHD and CGL equations consist of Galilean transformations and scalings. Noether’s second theorem is used to derive a wave action conservation equation for a linear non-WKBJ Alfvén waves model for stellar winds. Recent symmetry group investigation of the Lagrangian MHD equations in two space dimensions are discussed.

show abstract

Noether’s theorems and conservation laws in magnetohydrodynamics and Chew–Goldberger–Low plasmas

Webb,

Anco,

Meleshko

et al. 2024

Rev. Mod. Plasma Phys.

View full text Add to dashboard Cite

show abstract

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Zaidni,

Morrison,

Benjelloun

2024

Physica D: Nonlinear Phenomena

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Optimal control of port-Hamiltonian systems: Energy, entropy, and exergy

Philipp,

Schaller,

Worthmann

et al. 2024

Systems & Control Letters

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Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

Cited by 4 publications

References 59 publications

Noether’s theorems and conservation laws in magnetohydrodynamics and Chew–Goldberger–Low plasmas

Noether’s theorems and conservation laws in magnetohydrodynamics and Chew–Goldberger–Low plasmas

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Optimal control of port-Hamiltonian systems: Energy, entropy, and exergy

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