  Over a given regular domain of independent variables {x,y,z,t}, every
covariant vector field of flow can be constructed in terms a differential
1-form of Action. The associated Cartan topology permits the definition of four
basic topological equivalence classes of flows based on the Pfaff dimension of
the 1-form of Action. Potential flows or streamline processes are generated by
an Action 1-form of Pfaff dimension 1 and 2, respectively. Chaotic flows must
be associated with domains of Pfaff dimension 3 or more. Turbulent flows are
associated with domains of Pfaff dimension 4. It will be demonstrated that the
Navier-Stokes equations are related to Action 1-forms of Pfaff dimension 4. The
Cartan Topology is a disconnected topology if the Pfaff dimension is greater
than 2. This fact implies that the creation of turbulence (a state of Pfaff
dimension 4 and a disconnected Cartan topology) from a streamline flow (a state
of Pfaff dimension 2 and a connected topology) can take place only by
discontinuous processes which induce shocks and tangential discontinuities. On
the otherhand, the decay of turbulence can be described by continuous, but
irreversible, processes. Numerical procedures that force continuity of slope
and value cannot in principle describe the creation of turbulence, but such
techniques of forced continuity can be used to describe the decay of
turbulence.
