Topological Torsion Defects have been observed

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 IUTAM-SIMFLO conference in Copenhagen , it was stated that kinematically constrained physical systems which can be defined by a Lagrangian 1-form of Action, A, generate a non-compact 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 1-form of Action along the flow lines of the dynamical system generated by the Torsion vector, T, creates a 1-form 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 1-form that satisfies the constraints of a Navier-Stokes 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 non-zero four dimensional divergence of the Torsion vector generates its signature, curl v dot curlcurl v<> 0, a function [6] whose non-zero values define the domain of support for the 4D symplectic manifold. Topological Torsion defects in the Navier-Stokes 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 Navier-Stokes 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 hydrodynamic-thermodynamic experiments lead to the irreducible 4-dimensional qualities of nature, yet in a manner entirely different from the concepts generated by the Michelson-Morley 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.


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Last update 01/23/2009
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