2014/07/03 by Billy D. Jones, Jones, Billy D. · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.1407.1035
openalex publication_date 2014/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Navier-Stokes Hamiltonian is derived from first principles. Its Hamilton equations are shown to be equivalent to the continuity, Navier-Stokes, and energy conservation equations of a compressible viscous fluid. The derivations of the Euler and Navier-Stokes Hamiltonians are compared, with the former having identical dynamics to the Euler equation with the viscosity terms of the Navier-Stokes equation dropped from the beginning. The two Hamiltonians have the same number of degrees of freedom in three spatial and one temporal dimension: six independent scalar potentials, but their dynamical fields are necessarily different due to a theory with dissipation not mapping smoothly onto one without. The dynamical coordinate field of a dissipative fluid is a vector field that stores the initial position of all of its fluid particles. Thus these appear to be natural coordinates for studying arbitrary separations of fluid particles over time. The classical similarity renormalization group is introduced and the first steps are carried out deriving a flow equation for the Navier-Stokes Hamiltonian. Finally, the symmetries of a nonrelativistic viscous fluid are discussed through its galilean algebra with dissipative canonical Poisson brackets.