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Lagrangian flow visualization of multiple co-axial co-rotating vortex rings

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Abstract

This paper, for the first time, experimentally observes the detailed interacting phenomena of multiple co-axial co-rotating vortex rings using the method of finite-time Lyapunov exponent field. Besides the most attractive leapfrogging in dual vortex ring flows, several distinct phenomena are also found. The merger of squeezing is first observed in multiple vortex rings, resulting from the strong axial compressive induced effect. The inner vortex ring becomes axis-touching and cannot recover to the previous status. The merger due to elongation is already found in the previous studies. The inner vortex ring is elongated and distorted. The detachment of several independent vortex rings indicates that vortex merger has its limit, which is also a newfound phenomenon.

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References

  1. Borisov AV, Kilin AA, Mamaev IS (2013) The dynamics of vortex rings: leapfrogging, choreographies and the stability problem. Regul Chaotic Dyn 18:33

  2. Borisov AV, Kilin AA, Mamaev IS, Tenenev VA (2014) The dynamics of vortex rings: leapfrogging in an ideal and viscous fluid. Fluid Dyn Res 46(031):415

  3. Cheng M, Lou J, Lim TT (2015) Leapfrogging of multiple coaxial viscous vortex rings. Phys Fluids 27(031):702

  4. Farazmanda M, Haller G (2016) Polar rotation angle identifies elliptic islands in unsteady dynamical systems. Physica D 315:1–12

  5. Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140

  6. Haller G (2001) Distinguished material surfaces and coherent structures in three-dimensional flows. Physica D 149:248–277

  7. Haller G (2002) Lagrangian coherent structures from approximate velocity data. Phys Fluids 14:1851–1861

  8. Haller G (2015) Lagrangian coherent structures. Annu Rev Fluid Mech 47:137–62

  9. Haller G, Hadjighasem A, Farazmand M, Huhn F (2016) Defining coherent vortices objectively from the vorticity. J Fluid Mech 795:136–173

  10. Helmholtz H (1858) Über integrale der hydrodynamischen gleichungen, welche den wirbelbewegungen entsprechen. J Reine Angew Math 1858:25–55

  11. Hicks WM (1922) On the mutual threading of vortex rings. Proc R Soc Lond Ser A Contain Paper Math Phys Character 102:111–131

  12. Huhn F, van Rees WM, Gazzola M, Rossinelli D, Haller G, Koumoutsakos P (2015) Quantitative flow analysis of swimming dynamics with coherent lagrangian vortices. Chaos 25(087):405

  13. Jeong J, Hussain F (1995) Optimal vortex formation as a unifying principle in biological propulsion. J Fluid Mech 285:69–94

  14. Lim TT (1997) A note on the leapfrogging between two coaxial vortex rings at low reynolds number. Physica Fluids 9:239–41

  15. Mariani R, Kontis K (2010) Experimental studies on coaxial vortex loops. Phys Fluids 22(126):102

  16. Maxworthy T (1972) The structure and stability of vortex rings. J Fluid Mech 51:15–32

  17. Meleshko VV, Konstantinov MY, Gurzhi AA, Konovaljuk TP (1992) Advection of a vortex pair atmosphere in a velocity field of point vortices. Phys Fluids 4:2779

  18. O’Farrell C, Dabiri JO (2010) A lagrangian approach to identifying vortex pinch-off. Chaos 20(017):513

  19. Oshima Y (1975) Interaction of two vortex rings moving along a common axis of symmetry. J Phys Soc Jpn 38:1159–66

  20. Oshima Y (1978) The game of passing-through of a pair of vortex rings. J Phys Soc Jpn 45:660–4

  21. Satti J, Peng J (2013) Leapfrogging of two thick-cored vortex rings. Fluid Dyn Res 45(035):503

  22. Shadden SC, Lekien F, Marsden JE (2005) Definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensinal aperiodic flows. Phys D 212:271–304

  23. Shadden SC, Dabiri JO, Marsden JE (2006) Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys Fluids 18(047):105

  24. Yamada H, Matsui T (1978) Preliminary study of mutual slip-through of a pair of vortices. Phys Fluids 21:292

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Acknowledgements

Financial support from the State Key Development Program of Basic Research of China (2014CB744802) is gratefully acknowledged. Besides, this work was also supported by NSFC Project (91441205). The authors would also like to acknowledge the Center for High Performance Computing of Shanghai Jiao Tong University for providing the super computer-\(\pi\) to support this research.

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Correspondence to Hong Liu.

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Qin, S., Liu, H. & Xiang, Y. Lagrangian flow visualization of multiple co-axial co-rotating vortex rings. J Vis 21, 63–71 (2018) doi:10.1007/s12650-017-0450-6

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Keywords

  • FTLE
  • Vortex ring
  • Leapfrogging
  • Merger