Clebsch parameterization: Basic properties and remarks on its applications

DOI10.1063/1.3256125zbMath1304.58002OpenAlexW2047350863MaRDI QIDQ3583697

Zensho Yoshida

Publication date: 17 August 2010

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3256125

zbMATH Keywords

boundary-value problemsClebsch parameterizationstructural properties of vector fields

Mathematics Subject Classification ID

Differential forms in global analysis (58A10) Foundations of fluid mechanics (76A02)

Related Items (11)

Vorticity equation on surfaces with arbitrary topology embedded in three-dimensional Euclidean space ⋮ A generalized Clebsch transformation leading to a first integral of Navier-Stokes equations ⋮ Optical knots and contact geometry. I: From Arnol'd inequality to Ranada's dyons ⋮ The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space ⋮ Degenerate Laplacian describing topologically constrained diffusion: helicity constraint as an alternative to ellipticity ⋮ Gauge symmetries and Noether charges in Clebsch-parameterized magnetohydrodynamics ⋮ On magnetohydrodynamic gauge field theory ⋮ Nested invariant tori foliating a vector field and its curl: Toward MHD equilibria and steady Euler flows in toroidal domains without continuous Euclidean isometries ⋮ Nonlinear ion acoustic waves scattered by vortexes ⋮ Study of the 3D Euler equations using Clebsch potentials: dual mechanisms for geometric depletion ⋮ Singular Casimir elements of the Euler equation and equilibrium points

Cites Work

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• Differential forms in manifolds with boundary
• Hamiltonian description of the ideal fluid
• Semidirect Products and Reduction in Mechanics
• Evaluation of the structure of ergodic fields
• Plasma equilibrium with rational magnetic surfaces
• Gauging  the fluid
• Hidden symmetries in (relativistic) hydrodynamics
• The Green's and Neumann's Problems for Differential Forms on Riemannian Manifolds

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