Sverre O. Smalø, Norwegian University of Science and Technology (Trondheim, Norvegia)
Degenerations and other orderings on the space of d-dimensional representations of associative algebras
Monday, June 04 2007, at 17:00
Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza | |
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Timothy J. Sluckin, University of Southampton (Gran Bretagna)
The mathematical legacy of Vito Volterra
Tuesday, May 22 2007, at 17:00
Dipartimento di Matematica - Politecnico di Milano - Via Bonardi 9 - Milano - Aula Seminari VI piano | |
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Erik Weyer, University of Melbourne (Australia)
Non-asymptotic confidence regions for the parameters of dynamical systems
Tuesday, May 22 2007, at 14:30
Dipartimento di Matematica - Politecnico di Milano - Via Bonardi 9 - Milano - Aula Seminari MOX (VI piano) | |
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Carlo Petronio, Università di Pisa
Combinatorial and geometric methods in topology
Monday, April 23 2007, at 17:00
Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza | |
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Enzo Mitidieri, Università di Trieste
Convexity, representation and Liouville theorems
Monday, March 26 2007, at 17:00
Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza | |
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Yasuhide Fukumoto, Kyushu University (Giappone)
Asymptotic formula for velocity of a vortex ring and kinematic variational principle
Wednesday, March 14 2007, at 11:00
Dipartimento di Matematica ed Applicazioni - Università degli Studi di Milano Bicocca - Via Cozzi 53 -Milano Aula 3014 |
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Abstract
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A general formula is established for translation speed of an axisymmetric vortex ring whose core is not necessarily thin. We rely on Lamb-Saffman-Rott-Cantwell's method of calculating the total kinetic energy of fluid in two ways. Combined with the Navier-Stokes equations, we can skip the detailed solution for the flow field to extend Saffman's velocity formula of a viscous vortex ring to third order in the ratio of the core radius to the ring radius, a small parameter, for the entire range of the Reynolds number. At small Reynolds numbers, a solution that describes the whole life of a vortex ring is available. For inviscid motion, a further simplification is achieved by resorting to the variation, under the topological constraints, of the kinetic energy with respect to the hydrodynamic impulse. This principle bears similarity with the variational principle for a vortex ring governed by the Gross-Pitaevskii equation. Similarity is also found with Rasetti-Regge's theory for the three-dimensional motion of a vortex filament. |
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