It is a rare thing to attend a conference where on one day a new theoretical
prediction is made, and then on the following day experimental evidence is
presented to support the abstract theory. At the May 27,1997 meeting of the DTU
IUTAMSIMFLO conference in Copenhagen , it was stated that kinematically
constrained physical systems which can be defined by a Lagrangian 1form of
Action, A, generate a noncompact symplectic manifold of Pfaff (topological)
dimension 2n+2. For each specific physical system, there exists a unique vector
field, T, defined as the Torsion current. According to Cartan's magic formula,
evolution of the 1form of Action along the flow lines of the dynamical system
generated by the Torsion vector, T, creates a 1form of heat, Q, which does not
satisfy the Frobenious integrability condition. Therefore no integrating factor
exists and all such processes generated by Tmust be irreversible in a
thermodynamic sense.
It was demonstrated also that for an Action 1form that satisfies the
constraints of a NavierStokes fluid, the Topological Torsion vector would be
represented by lines of vorticity in the form of twisted helices in a space of
topological dimension 2n+2=4. The nonzero four dimensional divergence of the
Torsion vector generates its signature, curl v dot curlcurl v<> 0, a function
[6] whose nonzero values define the domain of support for the 4D symplectic
manifold. Topological Torsion defects in the NavierStokes fluid are represented
by the singular sets of this function.
The following day, the Russian scientists, P. A. Kuibin and V. Okulov,
presented experimental evidence of, and extensive measurements on, helical
twisted lines of vorticity in a swirling fluid. They also presented an
interesting analysis of the singular solution sets in an axisymmetric swirling
NavierStokes fluid, indicating the existence of a coherent structure formed
from helical torsional waves of opposite parity, a result also in agreement with
the concept of topological torsion. Then on the following day  by private
communication to this author  they conveyed the result that their analysis
indeed satisfied the signature equation of topological torsion, curl v dot
curlcurl v<> 0.
The physical importance of such results is that these experiments lend support to arguments that turbulence and other thermodynamically irreversible processes are inherent artifacts of a space of topological dimension greater than 3. It is remarkable that such hydrodynamicthermodynamic experiments lead to the irreducible 4dimensional qualities of nature, yet in a manner entirely different from the concepts generated by the MichelsonMorley experiments.
From a practical point of view for those researchers interested in reducing
drag, dissipation and noise, these results should focus attention on the primary
problem, that of eliminating or minimizing the source of four dimensional
topological torsion defects.
