Although there is not a precise definition of the turbulent state, almost
everyone intuitively recognizes Turbulence. A key feature that everyone agrees
upon is that turbulence is irreversible. From the argument that irreversibility
implies changing topology, then turbulence must be #associated with topological
From another point of view it is intuitive that Turbulence is "chaotic", but it
is also true that there exist chaotic systems that don't appear to be turbulent.
The Cartan calculus can be used to make precise the difference #between Chaos
and Turbulence. For chaos the integral of the