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Metric structures of laminar flows

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  • Pasmanter, Rubén A.

Abstract

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.

Suggested Citation

  • Pasmanter, Rubén A., 1998. "Metric structures of laminar flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 258(3), pages 311-328.
    • Handle: RePEc:eee:phsmap:v:258:y:1998:i:3:p:311-328
    DOI: 10.1016/S0378-4371(98)00254-4
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