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Many-Body Treatment of Navier-Stokes Fluids.
Final rept. May 85-Sep 86,
DAYTON UNIV OH RESEARCH INST
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A Lagrangian has been developed that is equivalent to the full Navier Stokes NS equation for a three-dimensional, subsonic single-component fluid, including viscous pressure gradients and advective terms. Dissipation is incorporated into the Lagrangian by using hypercomplex fields for the velocity potentials. This Lagrangian has been used to derive a field-theory description of fluid flow based on a diagonalized Hamiltonian and the corresponding Poisson-bracket relations. Greens functions for the linearized system and rules for drawing diagrams have been worked out. Perturbation expansions based on the linearized Hamiltonian converge as the Mach number, rather than as the Reynolds number as in earlier attempts to formulate Hamiltonians for the NS equation. This is achieved by expressing the Hamiltonian in terms of the velocity potentials, rather than directly in terms of the velocity fields. The interaction terms in the diagonalized Hamiltonian are of the same form as that for the electron-phonon interaction in quantum field theory. Keywords Field theory Turbulence Many-body theory Navier-Stokes equation.
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