Quasi-static solutions for quantum vortex motion under the localized induction approximation

Journal of Fluid Mechanics

Volumn 477, Issue , 2003, Pages 321-337

  Lipniacki, Tomasz ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; INTEGRATION; MATHEMATICAL TRANSFORMATIONS; ROTATION; VECTORS;

LOCALIZED INDUCTION APPROXIMATION (LIA);

FLUID DYNAMICS;

EQUATION; FLUID MECHANICS; MATHEMATICAL ANALYSIS; QUANTUM MECHANICS; SUPERFLUID; VELOCITY; VORTEX FLOW;

EID: 0037465216     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112002003282     Document Type: Article

References (18)

1. BARENGHI, C. F., BAUER, G. H., DONNELLY, R. J. & SAMUELS, D. C. 1997 Superfluid vortex lines in a model of turbulent flow. Phys. Fluids 9, 2631-2643.
2. HASIMOTO, H. 1972 A soliton on a vortex filament. J. Fluid Mech. 51, 477-485.
3. IDOWU, O. C., KIVOTIDES, D., BARENGHI, C. F. & SAMUELS, D. C. 2000 Equation for self-consistent superfluid vortex line dynamics. J. Low. Temp. Phys. 120, 269-280.
4. LANGER, J. & PERLINE, R. 1991 Poisson geometry of the filament equation. J. Nonlinear Sci. 1, 71-93.
5. 4He. Arch. Mech. 53, 23-43.
6. 4He. Phys. Rev. B 64, 214516-1-9.
7. LIPNIACKI, T. 2002 Self similar solutions of quantum vortex motion. In Advances in Turbulence IX. Proc. Ninth European Turbulence Conf. (ed. I. P. Castro, P. E. Hancock & T. G. Thomas), pp. 665-668. CIMNE.
8. NAKAYAMA, K., SEGUR, H. & WADATI, M. 1992 Integrability and the motion of curves. Phys. Rev. Lett. 69, 2603-2606.
9. NEMIROWSKII, S. K. & FISZDON, W. 1995 Chaotic quantized vortices and hydrodynamic processes in superfluid helium. Rev. Mod. Phys. 67, 37-84.
10. ONUKI, A. 1985 Line motion in terms of nonlinear Schrödinger equations. Prog. Theor. Phys. 74, 979-996.
11. RICCA, R. L. 1991 Intrinsic equations for the kinematics of a classical vortex string in higher dimensions. Phys. Rev. A 43, 4281-4288.
12. RICCA, R. L. 1992 Physical interpretation of certain invariants for vortex filament motion under LIA. Phys. Fluids A 4, 938-944.
13. RICCA, R. L. 1994 The effect of torsion on the motion of a helical vortex filament. J. Fluid Mech. 273, 241-259.
14. RICCA, R. L. 1996 The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics. Fluid Dyn. Res. 18, 245-268.
15. RICCA, R. L., SAMUELS, D. C. & BARENGHI, C. F. 1999 Evolution of vortex knots. J. Fluid. Mech. 391, 29-44.
16. 4He: line-line and line-boundary interactions. Phys. Rev. B 31, 5782-5804.
17. 4He: homogeneous superfluid turbulence. Phys. Rev. B 38, 2398-2417.
18. SCHWARZ, K. W. & ROSEN, J. R. 1991 Transient behavior of superfluid turbulence in a large channel. Phys. Rev. B 44, 7563-7577.