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 evolution. (see
Cartan's Topological Structure).

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
Topological Torsion is not zero, while for turbulence, the integral of Topological Parity is not zero.

	Downloads
	topturb.pdf 95k	.tex NA