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

• Type: Chapter or Part of a Book
• Date: 1993

Authors

Sílvio Gama (Author) FEUP; U. Frisch (Author) Other

Book

Title: Theory of Solar and Planetary Dynamos

Pages: 115-119

Publisher: Cambridge University Press (CUP)

Other information

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.

Language: Portuguese

Type (Professor's evaluation): Scientific

No. of pages: 5