Metric structures of laminar flows

An intrinsic metric tensor, two flat, conjugate connections and the corresponding distance-like function are constructed in the configuration space formed by the velocity field and the thermodynamic variables of a fluid in local thermal equilibrium. 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 connections are not metric-compatible. These results are achieved by applying the formalism of statistical manifolds (Amari, 1985, Differential-Geometrical methods in Statistics, Vol. 28, Springer; Amari et al., 1987, Inst. Math Statistics, Vol. 10, Hayward, CA) to the statistical mechanics of a moving fluid.