๐ŸซงOn Bubble Rings and Ink Chandeliers

On Bubble Rings and Ink Chandeliers

published in ACM Transactions on Graphics (SIGGRAPH 2019), Jul. 2019
Marcel Padilla
TU Berlin
Albert Chern
UC San Diego
Felix Knรถppel
TU Berlin
Ulrich Pinkall
TU Berlin
Peter Schrรถder

Left part: the reconnection of two bubble rings. Our algorithm output (left) vs real life footage (right).
Right part: the breakdown of an inkdrop into an ink chandelier. Real footage (left) vs our output (right).

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We introduce variable thickness, viscous vortex filaments. These can model such varied phenomena as underwater bubble rings or the intricate "chandeliers" formed by ink dropping into fluid. Treating the evolution of such filaments as an instance of Newtonian dynamics on a Riemannian configuration manifold we are able to extend classical work in the dynamics of vortex filaments through inclusion of viscous drag forces. The latter must be accounted for in low Reynolds number flows where they lead to significant variations in filament thickness and form an essential part of the observed dynamics. We develop and document both the underlying theory and associated practical numerical algorithms.


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This work was supported in part by the DFG Collaborative Research Center TRR 109 "Discretization in Geometry and Dynamics," the Caltech Center for Information Science and Technology, and the Einstein Foundation Berlin. Additional support was provided by SideFX software.


  author = {Padilla, Marcel and Chern, Albert and Kn\"{o}ppel, Felix and Pinkall, Ulrich and Schr\"{o}der, Peter},
  title = {On Bubble Rings and Ink Chandeliers},
  journal = {ACM Trans. Graph.},
  issue_date = {July 2019},
  volume = {38},
  number = {4},
  month = jul,
  year = {2019},
  issn = {0730-0301},
  pages = {129:1--129:14},
  articleno = {129},
  numpages = {14},
  url = {http://doi.acm.org/10.1145/3306346.3322962},
  doi = {10.1145/3306346.3322962},
  acmid = {3322962},
  publisher = {ACM},
  address = {New York, NY, USA},
  keywords = {differential geometry, fluid simulation, geodesics, physical modeling, vortex filaments, vorticity methods},