"Compact Dissipative Flow Structures with Topological Coherence Embedded in
Eulerian Environments", in: Non-linear Dynamics of Structures, edited by R.Z.
Sagdeev, U. Frisch, F. Hussain, S. S. Moiseev and N. S. Erokhin, (World
Scientific Press, Singapore ) p.139-164. (1991)

**Abstract: **Large scale secondary flow structures with compact boundary
surfaces can be generated in the interior of a Navier Stokes fluid. These
deformable topologically coherent structures have topological features different
from their environment and may have a long metastable lifetime even in viscous
media. An analytic example is given in terms of a parametric variation of an
exact closed form solution to the Navier-Stokes equations that exhibits a
saddle-node Hopf bifurcation. As the flow parameter is varied, the intially
unidirectional flow develops a reentrant secondary flow, or torsion defect, with
the appearance of a large scale structure confioned within a compact ellipsoidal
surface. As the secondary flow defect is created, the surface of null helicity
density undergoes a topological phase transition. The visual effect is
reminiscent of the "Vortex Bursting" propblem, but for the example flow, the
vorticity of the flow is an abolute invariant of the flow parameter. A theory
of continuous topological evolution is presented.