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Creation of an isolated turbulent blob fed by vortex rings

Nature Physics volume 19, pages 1193–1200 (2023)Cite this article

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Abstract

Turbulence is hard to control. Many experimental methods have been developed to generate this elusive state of matter, leading to fundamental insights into its statistical and structural features as well as its onset. In all cases, however, the material boundaries of the experimental apparatus pose a challenge for understanding what the turbulence has been fed and how it would freely evolve. Here we build and control a confined state of turbulence using elemental building blocks—vortex rings. We create a stationary and isolated blob of turbulence in a quiescent environment, initiated and sustained solely by vortex rings. We assemble a full picture of its three-dimensional structure, onset, energy budget and tunability. The incoming vortex rings can be endowed with conserved quantities, such as helicity, which can then be controllably transferred to the turbulent state. Our one-eddy-at-a-time approach opens the possibility for sculpting turbulent flows much as a state of matter, placing the turbulent blob at the targeted position, localizing it and ultimately harnessing it.

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Fig. 1: Generation of turbulence using vortex rings and their resistance to confinement.
Fig. 2: Two phases emerge as eight vortex rings repeatedly collide: coherent reconnections and a confined state of turbulence.
Fig. 3: Turbulent flow statistics and energy balance in a turbulent blob.
Fig. 4: Vring/(Rringf) governs the transition from coherent reconnections to turbulence.
Fig. 5: Repeated collision of helical rings transfers helicity to turbulence in a controlled fashion.

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Data availability

The data contained in the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

Code availability

The codes to handle 2D PIV and 3D PTV data, to compute energy spectra, structure functions and dissipation from velocity fields, and to visualize flows are available from the corresponding author upon reasonable request.

References

  1. Van Dyke, M. An Album of Fluid Motion Vol. 176 (Parabolic, 1982).

  2. von Kármán, T. Aerodynamics Vol. 9 (McGraw-Hill, 1963).

  3. Smits, A. J., McKeon, B. J. & Marusic, I. High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375 (2011).

    ADS  MATH  Google Scholar 

  4. Adrian, R. J. Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301 (2007).

    ADS  MATH  Google Scholar 

  5. Christensen, K. T. & Adrian, R. J. Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443 (2001).

    ADS  MATH  Google Scholar 

  6. Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396 (1999).

    ADS  MathSciNet  MATH  Google Scholar 

  7. Acarlar, M. & Smith, C. A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41 (1987).

    ADS  Google Scholar 

  8. Acarlar, M. & Smith, C. A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83 (1987).

    ADS  Google Scholar 

  9. Saddoughi, S. G. & Veeravalli, S. V. Local isotropy in turbulent boundary layers at high reynolds number. J. Fluid Mech. 268, 333–372 (1994).

    ADS  Google Scholar 

  10. Theodorsen, T. Mechanism of turbulence. In Proc. Second Midwestern Conference on Fluid Mechanics 1–19 (Ohio State Univ., 1952).

  11. Reynolds, O. XXIX. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. 174, 935–982 (1883).

  12. Mullin, T. Experimental studies of transition to turbulence in a pipe. Annu. Rev. Fluid Mech. 43, 1–24 (2011).

    ADS  MathSciNet  MATH  Google Scholar 

  13. Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468 (2007).

    ADS  MathSciNet  MATH  Google Scholar 

  14. Hof, B., Juel, A. & Mullin, T. Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502 (2003).

    ADS  Google Scholar 

  15. Hurst, D. & Vassilicos, J. Scalings and decay of fractal-generated turbulence. Phys. Fluids 19, 035103 (2007).

    ADS  MATH  Google Scholar 

  16. Kistler, A. & Vrebalovich, T. Grid turbulence at large reynolds numbers. J. Fluid Mech. 26, 37–47 (1966).

    ADS  Google Scholar 

  17. Comte-Bellot, G. & Corrsin, S. Simple eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 48, 273–337 (1971).

    ADS  Google Scholar 

  18. Bodenschatz, E., Bewley, G. P., Nobach, H., Sinhuber, M. & Xu, H. Variable density turbulence tunnel facility. Rev. Sci. Instrum. 85, 093908 (2014).

    ADS  Google Scholar 

  19. de la Torre, A. & Burguete, J. Slow dynamics in a turbulent von kármán swirling flow. Phys. Rev. Lett. 99, 054101 (2007).

    ADS  Google Scholar 

  20. Volk, R., Calzavarini, E., Leveque, E. & Pinton, J.-F. Dynamics of inertial particles in a turbulent von kármán flow. J. Fluid Mech. 668, 223–235 (2011).

    ADS  MATH  Google Scholar 

  21. Labbé, R., Pinton, J.-F. & Fauve, S. Study of the von Kármán flow between coaxial corotating disks. Phys. Fluids 8, 914–922 (1996).

    ADS  Google Scholar 

  22. Krogstad, P.-Å & Davidson, P. Is grid turbulence saffman turbulence? J. Fluid Mech. 642, 373–394 (2010).

    ADS  MathSciNet  MATH  Google Scholar 

  23. Davidson, P. Turbulence: An Introduction for Scientists and Engineers (Oxford Univ. Press, 2015).

  24. Davidson, P. The role of angular momentum conservation in homogeneous turbulence. J. Fluid Mech. 632, 329–358 (2009).

    ADS  MathSciNet  MATH  Google Scholar 

  25. Saffman, P. Note on decay of homogeneous turbulence. Phys. Fluids 10, 1349–1349 (1967).

    ADS  Google Scholar 

  26. Landau, L. D. & Lifshitz, E. M. Fluid Mechanics: Landau and Lifshitz: Course of Theoretical Physics Vol. 6 (Elsevier, 2013).

  27. Crow, S. C. Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179 (1970).

    ADS  Google Scholar 

  28. Tsai, C.-Y. & Widnall, S. E. The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73, 721–733 (1976).

    ADS  MATH  Google Scholar 

  29. Le Dizes, S. & Laporte, F. Theoretical predictions for the elliptical instability in a two-vortex flow. J. Fluid Mech. 471, 169–201 (2002).

    ADS  MathSciNet  MATH  Google Scholar 

  30. Oshima, Y. Head-on collision of two vortex rings. J. Phys. Soc. Jpn 44, 328–331 (1978).

    ADS  Google Scholar 

  31. Lim, T. T. & Nickels, T. B. Instability and reconnection in the head-on collision of two vortex rings. Nature 357, 225–227 (1992).

    ADS  Google Scholar 

  32. McKeown, R., Ostilla-Mónico, R., Pumir, A., Brenner, M. P. & Rubinstein, S. M. Turbulence generation through an iterative cascade of the elliptical instability. Sci. Adv. 6, 2717 (2020).

    ADS  Google Scholar 

  33. Brenner, M. P., Hormoz, S. & Pumir, A. Potential singularity mechanism for the euler equations. Phys. Rev. Fluids 1, 084503 (2016).

    ADS  Google Scholar 

  34. McKeown, R., Ostilla-Mónico, R., Pumir, A., Brenner, M. P. & Rubinstein, S. M. Cascade leading to the emergence of small structures in vortex ring collisions. Phys. Rev. Fluids 3, 124702 (2018).

    ADS  Google Scholar 

  35. Ostilla-Mónico, R., McKeown, R., Brenner, M. P., Rubinstein, S. M. & Pumir, A. Cascades and reconnection in interacting vortex filaments. Phys. Rev. Fluids 6, 074701 (2021).

    ADS  Google Scholar 

  36. Kolmogorov, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Acad. Sci. URSS 30, 301–305 (1941).

    MathSciNet  Google Scholar 

  37. Kolmogorov, A. N. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high reynolds number. J. Fluid Mech. 13, 82–85 (1962).

    ADS  MathSciNet  MATH  Google Scholar 

  38. de Jong, J. et al. Dissipation rate estimation from PIV in zero-mean isotropic turbulence. Exp. Fluids 46, 499 (2008).

    Google Scholar 

  39. Xu, D. & Chen, J. Accurate estimate of turbulent dissipation rate using piv data. Exp. Therm. Fluid Sci. 44, 662–672 (2013).

    Google Scholar 

  40. Pope, S. B. Turbulent Flows (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  41. Cekli, H. E., Tipton, C. & van de Water, W. Resonant enhancement of turbulent energy dissipation. Phys. Rev. Lett. 105, 044503 (2010).

    ADS  Google Scholar 

  42. Verschoof, R. A., te Nijenhuis, A. K., Huisman, S. G., Sun, C. & Lohse, D. Periodically driven Taylor–couette turbulence. J. Fluid Mech. 846, 834–845 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

  43. von der Heydt, A., Grossmann, S. & Lohse, D. Response maxima in modulated turbulence. Phys. Rev. E 67, 046308 (2003).

    ADS  Google Scholar 

  44. von der Heydt, A., Grossmann, S. & Lohse, D. Response maxima in modulated turbulence. II. Numerical simulations. Phys. Rev. E 68, 066302 (2003).

    ADS  Google Scholar 

  45. Kuczaj, A. K., Geurts, B. J. & Lohse, D. Response maxima in time-modulated turbulence: direct numerical simulations. Europhys. Lett. 73, 851 (2006).

    ADS  Google Scholar 

  46. Lohse, D. Periodically kicked turbulence. Phys. Rev. E 62, 4946 (2000).

    ADS  Google Scholar 

  47. Crow, S. C. & Champagne, F. Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591 (1971).

    ADS  Google Scholar 

  48. Kraichnan, R. H. Helical turbulence and absolute equilibrium. J. Fluid Mech. 59, 745–752 (1973).

    ADS  MATH  Google Scholar 

  49. Alexakis, A. Helically decomposed turbulence. J. Fluid Mech. 812, 752–770 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  50. Xavier, R. P., Teixeira, M. A. & da Silva, C. B. Asymptotic scaling laws for the irrotational motions bordering a turbulent region. J. Fluid Mech. 918, A3 (2021).

    ADS  MathSciNet  MATH  Google Scholar 

  51. Bisset, D. K., Hunt, J. C. & Rogers, M. M. The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410 (2002).

    ADS  MathSciNet  MATH  Google Scholar 

  52. Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230 (2009).

    ADS  MATH  Google Scholar 

  53. Chauhan, K., Philip, J., De Silva, C. M., Hutchins, N. & Marusic, I. The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119–151 (2014).

    Google Scholar 

  54. da Silva, C. B., Dos Reis, R. J. & Pereira, J. C. The intense vorticity structures near the turbulent/non-turbulent interface in a jet. J. Fluid Mech. 685, 165–190 (2011).

    ADS  MATH  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  56. Raffel, M. et al. Particle Image Velocimetry: A Practical Guide (Springer, 2018).

  57. Sciacchitano, A., Scarano, F. & Wieneke, B. Multi-frame pyramid correlation for time-resolved PIV. Exp. Fluids 53, 1087–1105 (2012).

    Google Scholar 

  58. Scarano, F. Iterative image deformation methods in piv. Meas. Sci. Technol. 13, R1 (2001).

    Google Scholar 

  59. Schanz, D., Gesemann, S. & Schröder, A. Shake-the-box: Lagrangian particle tracking at high particle image densities. Exp. Fluids 57, 70 (2016).

    Google Scholar 

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Acknowledgements

We thank N. Goldenfeld, G. Voth, F. Coletti and P. A. Davidson for insightful discussions and feedback and F. Coletti and L. Baker for discussion on the performance of PIV. We thank L. Biferale and F. Bonaccorso for sharing the simulation data of helical turbulence with us via the Smart-TURB database, as well as the Turbulence Research Group at Johns Hopkins University for access to the Johns Hopkins Turbulence Database. We also acknowledge Y. Ganan and R. Morton for help in performing the Gross-Pitavskii equation simulations. This work was supported by the Army Research Office through grant nos. W911NF-17-S-0002, W911NF-18-1-0046 and W911NF-20-1-0117, and by the Brown Science Foundation. We also acknowledge LaVision Inc. for support with PIV and PTV, and SideFX and Object Research Systems for granting software licences (for Houdini and Dragonfly, respectively) to visualize flows. The Chicago MRSEC is gratefully acknowledged for access to its shared experimental facilities (U.S. NSF grant DMR2011854). For access to computational resources, we thank the University of Chicago’s Research Computing Center and the University of Chicago’s GPU-based high-performance computing system (NSF DMR-1828629).

Author information

Author notes

  1. Noah P. Mitchell

    Present address: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, USA

  2. Stéphane Perrard

    Present address: PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, Paris, France

Authors and Affiliations

  1. James Franck Institute and Department of Physics, University of Chicago, Chicago, IL, USA

    Takumi Matsuzawa, Noah P. Mitchell, Stéphane Perrard & William T. M. Irvine

  2. Enrico Fermi Institute, University of Chicago, Chicago, IL, USA

    William T. M. Irvine

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  1. Takumi Matsuzawa
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Contributions

W.T.M.I. initiated and supervised research. S.P. designed chamber actuation and performed proof of concept experiments. N.P.M. contributed to chamber design and contributed analytical tools. T.M. constructed the apparatus and the imaging system, performed all experiments reported in this paper and wrote the code to handle, process and visualize flow data. T.M. and W.T.M.I. designed experiments, analysed data, performed modelling and wrote the paper.

Corresponding author

Correspondence to William T. M. Irvine.

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Nature Physics thanks Van Luc Nguyen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–49 and Tables I–IV.

Supplementary Video 1

This video displays coherent vortex reconnections that result in the generation of six outgoing secondary rings when eight vortex rings collide. The bubbles, generated by hydrolysis, indicate the location of the cores of the primary and the secondary rings. The video plays ten times slower than real time.

Supplementary Video 2

This video displays the irregular motion of the bubbles when the vortex rings are fired at 5 Hz, forming a turbulent blob. The first set of collisions resembles a single shot (Supplementary Video 1), yet the bubbles at the centre move more irregularly after a few cycles of vortex ring injection.

Supplementary Video 3

This video demonstrates the geometrical rule of vortex ring collisions when they are initialized on the plane of the platonic solids: the configuration of the ejecting, secondary rings is dual to the configuration of the primary rings.

Supplementary Video 4

The pathlines show that a single-shot collision of eight vortex rings results in the formation of six secondary rings, consistent with the GPE simulation (Supplementary Video 3). The trajectories are coloured by the vortex rings of origins. Notice that each secondary vortex ring consists of four colours, reflecting its four ‘parent’ vortex rings.

Supplementary Video 5

When a turbulent blob forms, the pathlines of particles that are transported by vortex rings become highly irregular due to turbulence within the blob. The ejecting pattern becomes more uniform than the case of coherent vortex reconnections. The colours are assigned by the vortex rings of origins. White trajectories are found in the turbulent blob, and are of unknown origins.

Supplementary Video 6

This visualization of a turbulent blob shows the formation of a steady, isolated region with considerably higher energy than its surroundings. Here, all detected pathlines are shown with opacity weighted by the speed. The slow particles (purple) are dimmed more than the fast (yellow) ones.

Supplementary Video 7

This video shows that the fluctuations dominate inside a turbulent blob (the blue cloud), whereas the time-averaged (mean) flow (the yellow cloud) is set up by the injected vortex rings outside the turbulent blob. The volume of the measured field is 120 mm × 102 mm × 100 mm with a voxel pitch of 2.2 mm.

Supplementary Video 8

These Mollweide plots show the normal component of each mass and enstrophy flux at the two phases. In the phase of coherent vortex reconnections (top row), the mass and enstrophy fluxes indicate focused ejection. When a turbulent blob is formed, the ejection is more uniform, and less enstrophy leaves the central region on average (bottom row). Here, a spherical surface with radius r ≈ 1.25Rblob = 30 mm is considered. The left column represents the normal mass flux Jm through the surface, and the right column is the normal enstrophy flux. The measurements correspond to (Vring/Rring, f) = (21 Hz, 0.2 and 4 Hz).

Supplementary Video 9

This video shows the energy and enstrophy fields of vortex ring collisions on the central slice, obtained by 2D PIV. The vortex reconnections generate secondary rings, four of which are visible in this video. Time averaging these fields provides equivalent pictures as Supplementary Fig. 2b,c.

Supplementary Video 10

This video shows the energy and enstrophy fields of vortex ring collisions in the state of a turbulent blob on the central slice, obtained by 2D PIV. Contrary to the single-shot collision (Supplementary Video 9), energy and enstrophy remain relatively steady within a spherical blob, and they leave the central region only intermittently. Time averaging these fields provides equivalent figures as Supplementary Fig. 2f,g.

Supplementary Video 11

This video shows the Q criterion field during single-shot collisions. Weak, outgoing vortices are generated upon the collisions. The video plays three times slower than real time.

Supplementary Video 12

This video shows the Q criterion field when vortex rings are fired repeatedly. Outgoing vortices interact with incoming ones. Small vortices are constantly generated in the region where collision takes place. After 10–15 cycles, it reaches a steady state. The video plays three times slower than real time.

Supplementary Video 13

This video shows the spatio-temporal structure of a local dissipation rate as well as its spatial average as a function of time. Regions with a high dissipation rate are concentrated along threads with thickness of approximately ten times the Kolmogorov length scale η. Two white boxes indicate the other turbulence length scales: the transverse Taylor microscale λg and the integral scale L. The local dissipation rate is calculated from a rate-of-strain tensor. One PIV pixel corresponds to a half of the interrogation window in the PIV algorithm.

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Matsuzawa, T., Mitchell, N.P., Perrard, S. et al. Creation of an isolated turbulent blob fed by vortex rings. Nat. Phys. 19, 1193–1200 (2023). https://doi.org/10.1038/s41567-023-02052-0

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