R. M. Kiehn DTU IUTAM SIMFLO Conference May 1997
Cartan's theory of a global 1-form of Action on a projective variety permits the
algebraic evaluation of certain useful geometric and topological objects which
can be singular. The projective algebraic methods therefore lend themselves to
the development of a theory of coherent structures and defects in which the
concept of translational shear dislocations and rotational shear disclinations
can be put on equal footing. The topological methods not only lead to a precise
definition of coherent structures in fluids, but also produce a non-statistical
test for thermodynamic irreversibility on a symplectic manifold of dimension 4,
and therefore yield a necessary criteria for turbulence.
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