Geodesics and curvature of a group of diffeomorphisms and motion of an ideal fluid

F. Nakamura, Y. Hattori, T. Kambe

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

Motion of an ideal fluid is represented as geodesics on the group of all volume-preserving diffeomorphisms. An explicit form of the geodesic equation is presented for the fluid flow on a three-torus Riemannian connection, commutator and curvature tensor are given explicitly and applied to a couple of simple flows with the Beltrami property. It is found that the curvature is non-positive for the section of two ABC flows with different values of the constants (A, B and C). The study is an extension of the Arnold's results (1989) in the two-dimensional case to three-dimensional fluid motions.

Original languageEnglish
Article number003
Pages (from-to)L45-L50
JournalJournal of Physics A: Mathematical and General
Volume25
Issue number2
DOIs
Publication statusPublished - 1992
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

Fingerprint

Dive into the research topics of 'Geodesics and curvature of a group of diffeomorphisms and motion of an ideal fluid'. Together they form a unique fingerprint.

Cite this