Geometrical approach to fluid models

Journal Article · Sat Mar 01 04:00:00 EST 1997 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.872576· OSTI ID:467290

Kuvshinov, B N; Schep, T J ^[1]

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1. FOM-Instituut voor Plasmafysica Rijnhuizen, Association EURATOM-FOM, Postbus 1207, 3430 BE Nieuwegein (The Netherlands)

Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 467290
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 3 Vol. 4; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
DIFFERENTIAL GEOMETRY
FLUIDS
HAMILTONIANS
LIE GROUPS
MAGNETOHYDRODYNAMICS
PLASMA FLUID EQUATIONS
VORTICES