Local Helicity, a Material Invariant for the Odd-dimensional Incompressible Euler

• Tipo: Capítulo ou Parte de Livro
• Data: 1993

Autores

Sílvio Gama (Autor) FEUP; U. Frisch (Autor) Outra

Livro

Título: Theory of Solar and Planetary Dynamos

Páginas: 115-119

Editora: Cambridge University Press (CUP)

Outras Informações

Resumo (PT): We show that in any odd number of dimensions, the Euler equations of ideal incompressible fluid flow have scalar invariants along any fluid particle trajectory. In three dimensions, the helicity is the space-integral of this invariant. Our proof is elementary. We give an alternative, much more compact, Lie group demonstration (suggested by B.A. Khesin) wich is readily extended to the MHD case and provides D-dimensional generalizations of Elsasser¿s material invariant.

Abstract (EN): We show that in any odd number of dimensions, the Euler equations of ideal incompressible fluid flow have scalar invariants along any fluid particle trajectory. In three dimensions, the helicity is the space-integral of this invariant. Our proof is elementary. We give an alternative, much more compact, Lie group demonstration (suggested by B.A. Khesin) wich is readily extended to the MHD case and provides D-dimensional generalizations of Elsasser¿s material invariant.

Idioma: Português

Tipo (Avaliação Docente): Científica

Nº de páginas: 5