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Impulse of vortex knots from diagram projections

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Topological Dynamics in the Physical and Biological Sciences

By using methods based on the analysis of standard plane projections of complex tangles, we can extract geometric information and use it to determine the impulsive forces associated with vortex knots and links. This method relies on the interpretation of linear and angular momentum of ideal vortex filaments in terms of projected areas [1]. An immediate application of this method allows one to make predictive estimates of the evolution and dynamical features of vortex knots and links [2]. This will be illustrated by a number of examples, some related to well-known results from laboratory and numerical experiments, where vortex ring collisions and vortex linking have been studied, and some others, such as the production of a trefoil vortex knot, proposed as “thought” experiments [3].

[1] Ricca, R.L. (2008) Momenta of a vortex tangle by structural complexity analysis. Physica D 237 , 2223-2227.

[2] Ricca, R.L. (2009) Structural complexity and dynamical systems. In Lectures on Topological Fluid Mechanics (ed. R.L. Ricca), pp. 169-188. Springer-CIME Lecture Notes in Mathematics 1973. Springer-Verlag.

[3] Ricca, R.L. (2009) New developments in topological fluid mechanics. Nuovo Cimento C 32 , 185-192.

This talk is part of the Isaac Newton Institute Seminar Series series.

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