Fully nonlinear local induction equation describing the motion of a vortex filament in superfluid 4He

Journal of Fluid Mechanics

Volumn 707, Issue , 2012, Pages 585-594

  Van Gorder, Robert A ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Computational methods; Quantum fluids; Vortex dynamics

Indexed keywords

COMPUTATIONAL METHODS; CONTROL NONLINEARITIES; EQUATIONS OF MOTION; FRICTION; INTEGRAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM CHEMISTRY; VORTEX FLOW;

DEPENDENT VARIABLES; FOUR DIMENSIONAL SYSTEMS; INDUCTION EQUATIONS; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; NORMAL-FLUID VELOCITY; QUALITATIVE FEATURES; QUANTUM FLUIDS; VORTEX DYNAMICS;

NONLINEAR EQUATIONS;

COMPUTATIONAL FLUID DYNAMICS; EQUATION; VORTEX;

EID: 84866065751     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2012.308     Document Type: Article

References (20)

1. ARMS, R. J. & HAMA, F. R. 1965 Localized-induction concept on a curved vortex and motion of an elliptic vortex ring. Phys. Fluids 8, 553.
2. DA RIOS, L. S. 1906 Sul moto d'un liquido indefinite con un filetto vorticoso di forma qualunque. Rend. Circ. Mat. Palermo 22, 117.
3. DMITRIYEV, V. P. 2005 Helical waves on a vortex filament. Am. J. Phys. 73, 563.
4. HALL, H. E. & VINEN, W. F. 1956a The rotation of liquid helium II. I. Experiments on the propagation of second sound in uniformly rotating helium II. Proc. R. Soc. Lond. A 238, 204.
5. HALL, H. E. & VINEN, W. F. 1956fc The rotation of liquid helium II. II. The theory of mutual friction in uniformly rotating helium I. Proc. R. Soc. Lond. A 238, 215.
6. HASIMOTO, H. 1971 Motion of a vortex filament and its relation to elastica. J. Phys. Soc. Japan 31, 293.
7. KIDA, S. 1981 A vortex filament moving without change of form. J. Fluid Meek 112, 397.
8. LANDAU, L. D. & LIFSHITZ, E. M. 1959 Fluid Mechanics. Addison and Wesley.
9. LIPNIACKI, T. 2003 Quasi-static solutions for quantum vortex motion under the localized induction approximation. J. Fluid Meek 477, 321.
10. MAGGIONI, R, ALAMRI, S. Z., BARENGHI, C. F. & RICCA, R. L. 2009 Kinetic energy of vortex knots and unknots. Nuovo Cimento C 32, 133.
11. MAGGIONI, E, ALAMRI, S. Z., BARENGHI, C. F. & RICCA, R. L. 2010 Velocity, energy, and helicity of vortex knots and unknots. Phys. Rev. E 82, 026309.
12. RICCA, R. L. 1993 Torus knots and polynomial invariants for a class of soliton equations. Chaos 3, 83.
13. RICCA, R. L., SAMUELS, D. C. & BARENGHI, C. F. 1999 Evolution of torus knots. J. Fluid Meek 391, 29.
14. 4He: line-line and line-boundary interactions. Phys. Rev. B 31, 5782.
15. 4He: homogeneous superfluid turbulence. Phys. Rev. B 38, 2398.
16. 4He: reformulation in the extrinsic vortex-filament coordinate space. Phys. Rev. B 84, 012506.
17. SHIVAMOGGI, B. K. & VAN HEIJST, G. J. F. 2010 Motion of a vortex filament in the local induction approximation: reformulation of the Da Rios-Betchov equations in the extrinsic filament coordinate space. Phys. Lett. A 374, 1742.
18. UMEKI, M. 2010 A locally induced homoclinic motion of a vortex filament. Theor. Comput. Fluid Dyn. 24, 383.
19. VAN GORDER, R. A. 2011 Integrable stationary solution for the fully nonlinear local induction equation describing the motion of a vortex filament. Theor. Comput. Fluid Dyn., doi:10.1007/s00162-011-0244-8 (in press).
20. VAN GORDER, R. A. 2012 Motion of a vortex filament in the local induction approximation: a perturbative approach. Theor. Comput. Fluid Dyn. 26, 161-171.