Reconnection of Vortex Bundles Lines with Sinusoidally

Affiliation(s)

Department of Applied Mathematics, College of Applied Science, Taibah University, Al-Madinah Al-Munawarah, KSA.

Department of Applied Mathematics, College of Applied Science, Taibah University, Al-Madinah Al-Munawarah, KSA.

ABSTRACT

Using the vortex filament model with the full Biot-Savart law, we show that non-straight bundles of quantized vortex lines in*HeII* are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence in many cases. We show that, during the bundle reconnection process, Kelvin waves of large amplitude are generated, in agreement with previous work and with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows. The reconnection events lead to changes in velocities, radius, number of points and total length. The existence of reconnections was confirmed by other authors using the model of nonlinear Schr?dinger equation (NLSE). Our results are agreed with the finding of other authors and extension to our numerical experiments.

Using the vortex filament model with the full Biot-Savart law, we show that non-straight bundles of quantized vortex lines in

Cite this paper

S. Alamri and A. Alenezi, "Reconnection of Vortex Bundles Lines with Sinusoidally,"*Applied Mathematics*, Vol. 4 No. 6, 2013, pp. 945-949. doi: 10.4236/am.2013.46130.

S. Alamri and A. Alenezi, "Reconnection of Vortex Bundles Lines with Sinusoidally,"

References

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[2] S. Z. Alamri, A. J. Youd and C. F. Barenghi, “Reconnection of Superfluid Vortex Bundles,” Physical Review Letters, Vol. 101, 2008, Article ID: 215302. doi:10.1103/PhysRevLett.101.215302

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[4] R. J. Donnelly, “Quantized Vortices In Helium II,” Cambridge University Press, Cambridge, 1991.

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[7] A. C. White, C. F. Barenghi and N. P. Proukakis, “Creation and Characterization of Vortex Clusters in Atomic Bose-Einstein Condensates,” Physical Review A, Vol. 86, 2012, Article ID: 013635. doi:10.1103/PhysRevA.86.013635

[8] C. F. Barenghi, “Turbulent Dissipation near Absolute Zero,” European Journal of Mechanics—B, Vol. 23, No. 3, 2004, pp. 415-425. doi:10.1016/j.euromechflu.2003.10.011

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[13] A. W. Baggaley and C. F. Barenghi, “Tree Method for Quantum Vortex Dynamics,” Journal of Low Temperature Physics, Vol. 166, No. 1-2, 2012, pp. 3-20. doi:10.1007/s10909-011-0405-6

[14] A. J. Allen, P. M. Chesler and H. Liu, “Holographic Vortex Liquids and Superfluid Turbulence,” arXiv Preprint [hep-th]: arXiv:1212.0281.

[15] A. W. Baggaley and C. F. Barenghi, “Turbulent Cascade of Kelvin Waves on Vortex Filaments,” Journal of Physics: Conference Series, Vol. 318, No. 6, 2011, Article ID: 062001. doi:10.1088/1742-6596/318/6/062001

[16] S. Z. Alamri, “A Numerical Study of Quantum Turbulence,” Ph.D. Dissertation, Newcastle University, Newcastle, 2009.

[17] M. S. Ismail and S. Z. Alamri, “Highly Accurate Finite Difference Method for Coupled Nonlinear Schrdinger Equation,” International Journal of Computer Mathematics, Vol. 81, No. 3, 2004, pp. 333-351. doi:10.1080/00207160410001661339

[18] F. Maggioni, S. Z. Alamri, C. Barenghi and R. Ricca, “Velocity, Energy, and Helicity of Vortex Knots and Unknots,” Physical Review E, Vol. 82, 2010, Article ID: 026309. doi:10.1103/PhysRevE.82.026309

[19] A. W. Baggaley, C. F. Barenghi and Y. A. Sergeev, “Quasiclassical and Ultraquantum Decay of Superfluid Turbulence,” Physical Review B, Vol. 85, 2012, Article ID: 060501(R). doi:10.1103/PhysRevB.85.060501

[20] M. V. Berry and M. R. Dennis, “Reconnections of Wave Vortex Lines,” European Journal of Physics, Vol. 33, No. 3, 2012, pp. 723-731. doi:10.1088/0143-0807/33/3/723

[21] D. Holm and R. Kerr, “Transient Vortex Events in the Initial Value Problem for Turbulence,” Physical Review Letters, Vol. 88, No. 24, 2002, Article ID: 244501. doi:10.1103/PhysRevLett.88.244501

[22] R. Kerr, “Cover Illustration: Vortex Structure of Euler Collapse,” Nonlinearity, Vol. 9, 1996, pp. 271-272. doi:10.1088/0951-7715/9/2/001

[23] J. Koplik and H. Levine, “Vortex Reconnection in Superfluid Helium,” Physical Review Letters, Vol. 71, No. 9, 1993, pp. 1375-1378. doi:10.1103/PhysRevLett.71.1375

[1] R. Aarts, “A Numerical Study of Quantized Vortices in He II,” Ph.D. Dissertation, Eindhoven University, Eindhoven, 1993.

[2] S. Z. Alamri, A. J. Youd and C. F. Barenghi, “Reconnection of Superfluid Vortex Bundles,” Physical Review Letters, Vol. 101, 2008, Article ID: 215302. doi:10.1103/PhysRevLett.101.215302

[3] C. F. Barenghi, R. J. Donnelly and W. F. Vinen, “Quantized Vortex Dynamics and Superuid Turbulence,” Springer, Berlin, 2001. doi:10.1007/3-540-45542-6

[4] R. J. Donnelly, “Quantized Vortices In Helium II,” Cambridge University Press, Cambridge, 1991.

[5] F. Maggioni, S. Z. Alamri, C. Barenghi and R. Ricca, “Kinetic Energy of Vortex Knots and Unknots,” Il Nuovo Cimento C, Vol. 32, 2009, p. 133.

[6] W. F. Vinen and J. J. Niemela, “Erratum: Quantum Turbulence,” Journal of Low Temperature Physics, Vol. 129, No. 5-6, 2002, pp. 213. doi:10.1023/A:1020890811263

[7] A. C. White, C. F. Barenghi and N. P. Proukakis, “Creation and Characterization of Vortex Clusters in Atomic Bose-Einstein Condensates,” Physical Review A, Vol. 86, 2012, Article ID: 013635. doi:10.1103/PhysRevA.86.013635

[8] C. F. Barenghi, “Turbulent Dissipation near Absolute Zero,” European Journal of Mechanics—B, Vol. 23, No. 3, 2004, pp. 415-425. doi:10.1016/j.euromechflu.2003.10.011

[9] A. W. Baggaley and C. F. Barenghi, “Condensate Fraction in Neutron Matter,” Physical Review E, Vol. 84, 2011, Article ID: 067301. doi:10.1103/PhysRevE.84.067301

[10] M. Tsubota, T. Araki and S. K. Nemirowskii, “Dynamics of Vortex Tangle Without Mutual Friction in Superfluid 4He,” Physical Review B, Vol. 62, No. 17, 2000, pp. 11751-11762. doi:10.1103/PhysRevB.62.11751

[11] K. W. Schwarz, “Three-Dimensional Vortex Dynamics in Superfluid 4He: Line-Line and Line-Boundary Interactions,” Physical Review B, Vol. 31, 1985, pp. 5782-5804. doi:10.1103/PhysRevB.31.5782

[12] K. W. Schwarz, “Three-Dimensional Vortex Dynamics in Superfluid 4He: Homogeneous Superfluid Turbulence,” Physical Review B, Vol. 38, No. 4, 1988, pp. 2398-2417. doi:10.1103/PhysRevB.38.2398

[13] A. W. Baggaley and C. F. Barenghi, “Tree Method for Quantum Vortex Dynamics,” Journal of Low Temperature Physics, Vol. 166, No. 1-2, 2012, pp. 3-20. doi:10.1007/s10909-011-0405-6

[14] A. J. Allen, P. M. Chesler and H. Liu, “Holographic Vortex Liquids and Superfluid Turbulence,” arXiv Preprint [hep-th]: arXiv:1212.0281.

[15] A. W. Baggaley and C. F. Barenghi, “Turbulent Cascade of Kelvin Waves on Vortex Filaments,” Journal of Physics: Conference Series, Vol. 318, No. 6, 2011, Article ID: 062001. doi:10.1088/1742-6596/318/6/062001

[16] S. Z. Alamri, “A Numerical Study of Quantum Turbulence,” Ph.D. Dissertation, Newcastle University, Newcastle, 2009.

[17] M. S. Ismail and S. Z. Alamri, “Highly Accurate Finite Difference Method for Coupled Nonlinear Schrdinger Equation,” International Journal of Computer Mathematics, Vol. 81, No. 3, 2004, pp. 333-351. doi:10.1080/00207160410001661339

[18] F. Maggioni, S. Z. Alamri, C. Barenghi and R. Ricca, “Velocity, Energy, and Helicity of Vortex Knots and Unknots,” Physical Review E, Vol. 82, 2010, Article ID: 026309. doi:10.1103/PhysRevE.82.026309

[19] A. W. Baggaley, C. F. Barenghi and Y. A. Sergeev, “Quasiclassical and Ultraquantum Decay of Superfluid Turbulence,” Physical Review B, Vol. 85, 2012, Article ID: 060501(R). doi:10.1103/PhysRevB.85.060501

[20] M. V. Berry and M. R. Dennis, “Reconnections of Wave Vortex Lines,” European Journal of Physics, Vol. 33, No. 3, 2012, pp. 723-731. doi:10.1088/0143-0807/33/3/723

[21] D. Holm and R. Kerr, “Transient Vortex Events in the Initial Value Problem for Turbulence,” Physical Review Letters, Vol. 88, No. 24, 2002, Article ID: 244501. doi:10.1103/PhysRevLett.88.244501

[22] R. Kerr, “Cover Illustration: Vortex Structure of Euler Collapse,” Nonlinearity, Vol. 9, 1996, pp. 271-272. doi:10.1088/0951-7715/9/2/001

[23] J. Koplik and H. Levine, “Vortex Reconnection in Superfluid Helium,” Physical Review Letters, Vol. 71, No. 9, 1993, pp. 1375-1378. doi:10.1103/PhysRevLett.71.1375