In this paper we review some results on geometric and topological vortex dynamics. After some background on flow maps, topological equivalence of frozen fields and conservation laws, we discuss geometric aspects of vortex filament motion (intrinsic equations, connections with integrable dynamics and extension to higher dimensional manifolds) and the topological interpretation of kinetic helicity in terms of linking numbers. We recall basic results on evolution of vortex knots and links and outline possible applications of algebraic, geometric and topological measures to evaluate structural complexity of vortex flows
Ricca, R. (2001). Geometric and topological aspects of vortex motion. In R.L. Ricca (a cura di), An introduction to the geometry and topology of fluid flows (Cambridge, 2000) (pp. 203-228). Springer.
Geometric and topological aspects of vortex motion
Ricca, R
2001
Abstract
In this paper we review some results on geometric and topological vortex dynamics. After some background on flow maps, topological equivalence of frozen fields and conservation laws, we discuss geometric aspects of vortex filament motion (intrinsic equations, connections with integrable dynamics and extension to higher dimensional manifolds) and the topological interpretation of kinetic helicity in terms of linking numbers. We recall basic results on evolution of vortex knots and links and outline possible applications of algebraic, geometric and topological measures to evaluate structural complexity of vortex flows
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
