Metric structures of inviscid flows
Abstract
Description
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.
20 pages, LaTeX. This version is almost identical to the one submitted for publication in October 1995
20 pages, LaTeX. This version is almost identical to the one submitted for publication in October 1995