Rub\'en A.\ Pasmanter
Metric structures of inviscid flows
(59K, LaTeX)
ABSTRACT. 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.