Compact Dissipative Flow Structures with Topological Coherence...

"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.


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