Many-Body Treatment of Navier-Stokes Fluids.
Abstract
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. Green's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1986
- Accession Number
- ADA188893
Entities
People
- Roger J. Becker
Organizations
- University of Dayton