Turbulence and the Navier-Stokes equations

Abstract

The concept of continuous topological evolution, based upon Cartan's methods of exterior differential systems, is used to develop a topological theory of non-equilibrium thermodynamics, within which there exist processes that exhibit continuous topological change and thermodynamic irreversibility. The technique furnishes a universal, topological foundation for the partial differential equations of hydrodynamics and electrodynamics; the technique does not depend upon a metric, connection or a variational principle. Certain topological classes of solutions to the Navier-Stokes equations are shown to be equivalent to thermodynamically irreversible processes.