The collision of two vortex rings

The case of the collision of two vortex rings was introduced to me via the work of Lim and Nickels (1992)1. In their lab setup, dyed fluid was injected such that two vortex rings emerged with trajectories laying on a path of a head-on collision. An experiment of theirs was filmed with a modest camera:

Such spectacular results would be a lot of fun to model, so I set out to recreate this setup with the Basilisk code. In order to prevent spurious transport of the tracer fluid, I opted to “dye” the fluid near the inlet with 200000 tracer particles for the visualization.

Inspired by this success, and its efficient computation on the adpative grid, I also (loosely) used this case as a problem to benchmark the fourth-order accurate I was developing2. In this particular scenario, the vortex rings were initialized at the start of the simulation. The result is shown below, using volumetric rendering of a vortex-detection field (the λ2\lambda_2 criterion of Jeong and Hussain (1995)3.

The ray-based visualization tool, called bwatch, which visualizes the octree solution data was developed by me for these types op visualizations.

References

  1. Lim, T. T., & Nickels, T. B. (1992). Instability and reconnection in the head-on collision of two vortex rings. Nature, 357(6375), 225-227.↩︎

  2. van Hooft, J. A., & Popinet, S. (2022). A fourth-order accurate adaptive solver for incompressible flow problems. Journal of Computational Physics, 462, 111251.↩︎

  3. Jeong, J., & Hussain, F. (1995). On the identification of a vortex. Journal of fluid mechanics, 285, 69-94.↩︎

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