Science Advances

Supplementary Materials

The PDF file includes:

  • Section S1. PIV analysis of vortex ring geometry
  • Section S2. Simulating vortex ring collisions using the Biot-Savart approximation
  • Section S3. Nonlinear development of the elliptical instability
  • Section S4. Interactions of secondary vortex filaments
  • Section S5. Analysis of the transfer of energy in a turbulent flow
  • Section S6. Emergence of turbulence from the elliptical instability with increasing Reynolds number
  • Section S7. Supplementary movie descriptions
  • Fig. S1. Vortex ring tracking and measurement through PIV.
  • Fig. S2. Vortex ring and core geometry.
  • Fig. S3. Modeling radial growth of colliding vortex rings.
  • Fig. S4. Onset of the elliptical instability for colliding vortex rings.
  • Fig. S5. Formation of a secondary vortex filament.
  • Fig. S6. Alternating structure of secondary filaments.
  • Fig. S7. Evolution of circulation.
  • Fig. S8. Interactions of secondary vortex filaments.
  • Fig. S9. Transition to turbulence in DNS of interacting vortex tubes.
  • Fig. S10. Vorticity evolution for DNS of interacting vortex tubes.
  • Legends for movies S1 to S11
  • References (3743)

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Other Supplementary Material for this manuscript includes the following:

  • Movie S1 (.mp4 format). Head-on collision of vortex rings.
  • Movie S2 (.mp4 format). Experimental vortex ring collision with dyed cores.
  • Movie S3 (.mp4 format). DNS of dyed vortex ring collision.
  • Movie S4 (.mp4 format). Experimental fully dyed vortex ring collision.
  • Movie S5 (.mp4 format). DNS of vortex tube interaction: ReΓ = 4500.
  • Movie S6 (.mp4 format). DNS of vortex tube interaction: ReΓ = 3500.
  • Movie S7 (.mp4 format). Interaction and splitting of secondary vortex filaments.
  • Movie S8 (.mp4 format). DNS of vortex tube interaction: ReΓ = 6000.
  • Movie S9 (.mp4 format). Iterative cascade of elliptical instabilities.
  • Movie S10 (.mp4 format). Gaussian fit to vortex core PIV data.
  • Movie S11 (.mp4 format). DNS of vortex tube interaction: ReΓ = 2000.

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