With this paper we want to pay tribute to 150 years of work on topological fluid mechanics. For this, we review Helmholtz's (1858) original contribution on topological issues related to vortex motion. Some recent results on aspects of structural complexity analysis of fluid flows are presented and discussed, as well as new results on topological bounds on the energy of magnetic knots and links in ideal magnetohydrodynamics, and on helicity-crossing number relations in dissipative fluids. © 2009 Springer-Verlag Berlin Heidelberg.
Ricca, R. (2009). Structural complexity and dynamical systems. In R. Ricca (a cura di), Lectures on Topological Fluid Mechanics (pp. 169-188). Springer.
Structural complexity and dynamical systems
RICCA, RENZO
2009
Abstract
With this paper we want to pay tribute to 150 years of work on topological fluid mechanics. For this, we review Helmholtz's (1858) original contribution on topological issues related to vortex motion. Some recent results on aspects of structural complexity analysis of fluid flows are presented and discussed, as well as new results on topological bounds on the energy of magnetic knots and links in ideal magnetohydrodynamics, and on helicity-crossing number relations in dissipative fluids. © 2009 Springer-Verlag Berlin Heidelberg.
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