Momenta of a vortex tangle by structural complexity analysis

Physica D: Nonlinear Phenomena

Volumn 237, Issue 14-17, 2008, Pages 2223-2227

  Ricca, Renzo L ^a,b  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

^b ISI FOUNDATION   (Italy)

Author keywords

Structural complexity; Vortex tangle

Indexed keywords

DYNAMICAL SYSTEMS; NUMERICAL METHODS; TOPOLOGY;

COMPLEXITY ANALYSIS; DYNAMICAL PROPERTIES; GEOMETRIC METHOD; INDUCTION APPROXIMATION; SCALE DISTRIBUTIONS; STRUCTURAL COMPLEXITY; TOPOLOGICAL PROPERTIES; VORTEX TANGLES;

VORTEX FLOW;

EID: 47049093277     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.01.002     Document Type: Article

References (20)

1. Euler L. Solutio problematis ad geometriam situs pertinentis. Commentarii Academie Scientiarum Imperialis Petropolitanae 8 (1741) 128-140
2. Alexanderson G.L. Euler and Königsberg's bridges: A historical view. Bull. Am. Math. Soc. 43 (2006) 567-573
3. (W. Thomson) L.K. On vortex atoms. Proc. R. Soc. Edin. 6 (1867) 94-105
4. Barenghi C.F., Ricca R.L., and Samuels D.C. How tangled is a tangle?. Physica D 157 (2001) 197-206
5. Ricca R.L. Structural complexity. In: Scott A. (Ed). Encyclopedia of Nonlinear Science (2005), New York and London, Routledge 885-887
6. 4He: Homogeneous superfluid turbulence. Phys. Rev. B 38 (1988) 2398-2417
7. Da Rios L.S. On the motion of an unbounded liquid with a vortex filament of any shape. Rend. Circ. Mat. Palermo 22 (1906) 117-135 (in Italian)
8. Arms R.J., and Hama F.R. Localized induction concept on a curved vortex and motion of an elliptic vortex ring. Phys. Fluids 8 (1965) 553-559
9. Fukumoto Y. On integral invariants for vortex motion under the localized induction approximation. J. Phys. Soc. Japan 56 (1987) 4207-4209
10. Ricca R.L. Physical interpretation of certain invariants for vortex filament motion under LIA. Phys. Fluids A 4 (1992) 938-944
11. Saffman P.G. Vortex Dynamics (1991), Cambridge University Press, Cambridge
12. Langevin R. Differential geometry of curves and surfaces. In: Ricca R.L. (Ed). An Introduction to the Geometry and Topology of Fluid Flows. NATO Science Series II vol. 47 (2001), Kluwer Academic Publs., Dordrecht 13-33
13. Gauss C.F. Letter to H. Olbers. Werke 8 (1825) 398-400
14. Fukumoto Y. Stationary configurations of a vortex filament in background flows. Proc. R. Soc. Lond. A 453 (1997) 1205-1232
15. Kiknadze L., and Mamaladze Yu. The waves on the vortex ring in He II. J. Low Temp. Phys. 126 (2002) 321-326
16. Barenghi C.F., Hänninen R., and Tsubota M. Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves. Phys. Rev. E 74 (2006) 1-5
17. Lim T.T., and Nickels T.B. Instability and reconnection in head-on collision of two vortex rings. Nature 357 (1992) 225-227
18. Moffatt H.K., and Ricca R.L. Interpretation of invariants of the Betchov-Da Rios equations and of the Euler equations. In: Jimenez J. (Ed). The Global Geometry of Turbulence (1992), Plenum Press, New York 257-264
19. W.S. Massey, Algebraic Topology: An Introduction, Harcourt, Brace and World, Inc., New York
20. R.L. Ricca, Structural complexity and dynamical systems, in: R.L. Ricca (Ed.), Lectures on Topological Fluid Mechanics, Springer-CIME Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2008 (in press)