Metric structures of inviscid flows

Details Metric structures of inviscid flows Metric structures of inviscid flows

1996-02-15

arxiv.org/abs/chao-dyn/9602016v2

Physica A 258 (1998) 311-328.

Nonlinear Sciences

Chaotic Dynamics

20 pages, LaTeX. This version is almost identical to the one submitted for publication in October 1995

Scientific paper

An intrinsic metric tensor, a flat connexion and the corresponding distance-like function are constructed in the configuration space formed by velocity field {\bf and} the thermodynamic variables of an inviscid fluid. The kinetic-energy norm is obtained as a limiting case; all physical quantities are Galilean invariant. Explicit expressions are given for the case of an ideal gas. The flat connexion is {\bf not} metric-compatible. These results are achieved by applying the formalism of statistical manifolds \cite{amari,otros} to the statistical mechanics of a moving fluid.

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