TY - JOUR

T1 - Geodesics and curvature of a group of diffeomorphisms and motion of an ideal fluid

AU - Nakamura, F.

AU - Hattori, Y.

AU - Kambe, T.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

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U2 - 10.1088/0305-4470/25/2/003

DO - 10.1088/0305-4470/25/2/003

M3 - Article

AN - SCOPUS:0005828977

SN - 0305-4470

VL - 25

SP - L45-L50

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 2

M1 - 003

ER -