research-article

On bubble rings and ink chandeliers

Authors:

Marcel Padilla,

Felix Knöppel,

Ulrich Pinkall,

Peter SchröderAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 38, Issue 4

Article No.: 129, Pages 1 - 14

https://doi.org/10.1145/3306346.3322962

Published: 12 July 2019 Publication History

Abstract

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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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.

More information is available at https://www3.math.tu-berlin.de/geometrie/wp_padilla/on_bubble_rings_and_ink_chandeliers/

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References

[1]

Alexis Angelidis and Fabrice Neyret. 2005. Simulation of Smoke based on Vortex Filament Primitives. In Proc. Symp. Comp. Anim. ACM, 87--96.

Digital Library

[2]

Vladimir I. Arnold and Boris A. Khesin. 1998. Topological Methods in Hydrodynamics. Springer.

Digital Library

[3]

Harry Bateman. 1915. Some Recent Researches on the Motion of Fluids. Mon. Weath. R. 43, 4 (1915), 163--170.

[4]

Mikl'os Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete Viscous Threads. ACM Trans. Graph. 29, 4 (2010), 116:1--10.

Digital Library

[5]

Peter S. Bernard. 2006. Turbulent Flow Properties of Large-scale Vortex Systems. PNAS 103, 27 (2006), 10174--10179.

[6]

Peter S. Bernard. 2009. Vortex Filament Simulation of the Turbulent Coflowing Jet. Phys. Fluids 21, 2 (2009).

[7]

Danielis Bernoulli. 1738. Hydrodynamica, sive de viribus et motibus fluidorum commentarii. Argentorati. For a modern account see also {Grattan-Guinness 2005} and {Darrigol and Frisch 2008}.

[8]

Jean-Baptiste Biot and Nicolas-Pierre-Antoine Savart. 1820. Note sur le Magnétisme de la pile de Volta. Annal. Chimie et Phys. 15 (1820), 222--223.

[9]

Tyson Brochu, Todd Keeler, and Robert Bridson. 2012. Linear-Time Smoke Animation with Vortex Sheet Meshes. In Proc. Symp. Comp. Anim. Eurographics Assoc., 87--95.

Digital Library

[10]

J. M. Burgers. 1948. A Mathematical Model Illustrating the Theory of Turbulence. Adv. Appl. Math. 1 (1948), 171--199.

[11]

Augustin-Louis Cauchy. 1815. Théorie de la Propagation des Ondes a la Surface d'un Fluide Pesant d'une Profondeur Indéfinie. In Oeuvres Complètes d'Augustin Cauchy. Vol. 1. Imprimerie Royale. Presented to the French Academy in 1815 (publ. 1827).

[12]

Ching Chang and Stefan G. Llewellyn Smith. 2018. The Motion of a Buoyant Vortex Filament. J. Fl. Mech. 857 (2018), R1:1--13.

[13]

M. Cheng, J. Lou, and T. T. Lim. 2013. Motion of a Bubble Ring in a Viscous Fluid. Phys. Fluids 25, 6 (2013), 067104:1--19.

[14]

Stephen Childress. 2009. An Introduction to Theoretical Fluid Dynamics. AMS.

[15]

Alexandre Joel Chorin. 1990. Hairpin Removal in Vortex Interactions. J. Comput. Phys. 91, 1 (1990), 1--21.

Digital Library

[16]

Alexandre Joel Chorin. 1993. Hairpin Removal in Vortex Interactions II. J. Comput. Phys. 107, 1 (1993), 1--9.

Digital Library

[17]

Fang Da, Christopher Batty, Chris Wojtan, and Eitan Grinspun. 2015. Double Bubbles Sands Toil and Trouble: Discrete Circulation-Preserving Vortex Sheets for Soap Films and Foams. ACM Trans. Graph. 34, 4 (2015), 149:1--9.

Digital Library

[18]

Fang Da, David Hahn, Christopher Batty, Chris Wojtan, and Eitan Grinspun. 2016. Surface-Only Liquids. ACM Trans. Graph. 35, 4 (2016), 78:1--12.

Digital Library

[19]

O. Darrigol and U. Frisch. 2008. From Newton's Mechanics to Euler's Equations. Phy. D: Nonl. Phenom. 237, 14--17 (2008), 1855--1869.

[20]

Uriel Frisch and Barbara Villone. 2014. Cauchy's almost Forgotten Lagrangian Formulation of the Euler Equation for 3D Incompressible Flow. Eu. Phy. J. H 39, 3 (2014), 325--351.

[21]

Sylvestre Gallot, Dominique Hulin, and Jacques Lafontaine. 2004. Riemannian Geometry (3<sup>rd</sup> ed.). Springer.

[22]

S. K. Godunov. 1959. A Difference Method for Numerical Calculation of Discontinuous Solutions of the Equations of Hydrodynamics. Mat. Sb. (N.S.) 47(89), 3 (1959), 271--306.

[23]

Ivor Grattan-Guinness (Ed.). 2005. Landmark Writings in Western Mathematics 1640--1940. Elsevier, Chapter Daniel Bernoulli: Hydrodynamica (G. K. Mikhailov), 131--142.

[24]

Ernst Hairer, Syvert Paul Nørsett, and Gerhard Wanner. 1993. Solving Ordinary Differential Equations I: Nonstiff Problems (2nd ed.). Springer.

Digital Library

[25]

Anton Izosimov and Boris Khesin. 2018. Vortex Sheets and Diffeomorphism Groupoids. Adv. Math. 338 (2018), 447--501.

[26]

Theodor Kaluza. 1921. Zum Unitätsproblem der Physik. Sitzungsber. Preuss. Akad. Wiss. Berlin (1921), 966--972. English translation in

[27]

Oskar Klein. 1926. Quantentheorie und Fünfdimensionale Relativitätstheorie. Z. für Phys. 37, 12 (1926), 895--906.

[28]

Eric Lauga and Thomas R. Powers. 2009. The Hydrodynamics of Swimming Microorganisms. Rep. Prog. Phys. 72 (2009), 096601:1--36.

[29]

Randall J. LeVeque. 2002. Finite-Volume Methods for Hyperbolic Problems. Cam. U. P.

[30]

Xiangyun Liao, Weixin Si, Zhiyong Yuan, Hanqiu Sun, Jing Qin, Qiong Wang, and Pheng-Ann Heng. 2018. Animating Wall-Bounded Turbulent Smoke via Filament-Mesh Particle-Particle Method. IEEE Trans. Vis. Comp. Graph. 24, 3 (2018), 1260--1273.

[31]

Christian Loeschke. 2012. On the Relaxation of a Variational Principle for the Motion of a Vortex Sheet in Perfect Fluid. Ph.D. Dissertation. Rhein. Fried.-Wilh.-Univ. Bonn.

[32]

T. S. Lundgren and W. T. Ashurst. 1989. Area-Varying Waves on Curved Vortex Tuibes with Application to Vortex Breakdown. J. Fl. Mech. 200 (1989), 283--307.

[33]

T. S. Lundgren and N. N. Mansour. 1988. Oscillations of Drops in Zero Gravity with Weak Viscous Effects. J. Fl. Mech. 194 (1988), 479--510.

[34]

T. S. Lundgren and N. N. Mansour. 1991. Vortex Ring Bubbles. J. Fl. Mech. 224 (1991), 177--196.

[35]

Jerrold Marsden and Alan Weinstein. 1983. Coadjoint Orbits, Vortices and Clebsch Variables for Incompressible Fluids. Phy. D: Nonl. Phenom. 7, 1--3 (1983), 305--323.

[36]

J. S. Marshall. 1991. A General Theory of Curved Vortices with Circular Cross-Section and Varialbe Core Area. J. Fl. Mech. 229 (1991), 311--338.

[37]

V. V. Meleshko, A. A. Gourjii, and T. S. Krasnopolskaya. 2012. Vortex Rings: History and State of the Art. J. Math. Sc. 187, 6 (2012), 772--808.

[38]

Derek William Moore and Philip Geoffrey Saffman. 1972. The Motion of a Vortex Filament with Axial Flow. Phil. Tr. R. Soc. Lond. A 272, 1226 (1972), 403--429.

[39]

T. J. Pedley. 1968. The Toroidal Bubble. J. Fl. Mech. 32, 1 (1968), 97--112.

[40]

Tobias Pfaff, Nils Thuerey, and Markus Gross. 2012. Lagrangian Vortex Sheets for Animating Fluids. ACM Trans. Graph. 31, 4 (2012), 112:1--8.

Digital Library

[41]

Bo Ren, Xu-Yun Yang, Ming C. Lin, Nils Thuerey, Matthias Teschner, and Chenfeng Li. 2018. Visual Simulation of Multiple Fluids in Computer Graphics: A State-of-the-Art Report. J. Comp. Sc. Tech. 33, 3 (2018), 431--451.

[42]

William B. Rogers. 1858. On the Formation of Rotating Rings by Air and Liquids under certain Conditions of Discharge. Am. J. Sc. A. 26, 77 (1858), 246--258.

[43]

Louis Rosenhead and Harold Jeffreys. 1930. The Spread of Vorticity in the Wake behind a Cylinder. Proc. R. Soc. Lond. A 127, 806 (1930), 590--612.

[44]

P. G. Saffman. 1992. Vortex Dynamics. Cam. U. P.

[45]

Karim Shariff and Anthony Leonard. 1992. Vortex Rings. Ann. Rev. Fl. Mech. 24 (1992), 235--279.

[46]

Michiko Shimokawa, Ryosei Mayumi, Taiki Nakamura, Toshiya Takami, and Hidetsugu Sakaguchi. 2016. Breakup and Deformation of a Droplet Falling in a Miscible Solution. Phys. R. E 93, 6 (2016), 062214:1--9.

[47]

Mark J. Stock, Werner J. A. Dahm, and Grétar Tryggvason. 2008. Impact of a Vortex Ring on a Density Interface using a Regularized Inviscid Vortex Sheet Method. J. Comput. Phys. 227, 21 (2008), 9021--9043. See also images at http://markjstock.com/#/chaoticescape/.

Digital Library

[48]

G. I. Taylor. 1953. Formation of a Vortex Ring by Giving an Impulse to a Circular Disk and then Dissolving it Away. J. Appl. Ph. 24, 1 (1953), 104--105.

[49]

J. J. Thomson. 1883. A Treatise on the Motion of Vortex Rings. Macmillan, London.

[50]

J. J. Thomson and H. F. Newall. 1886. On the Formation of Vortex Rings by Drops falling into Liquids, and some allied Phenomena. Proc. R. Soc. Lond. 39, 239--241 (1886), 417--436.

[51]

Charles Tomlinson. 1864. LXV. On a New Vareity of the Cohesion-Figures of Liquids. Lon. Edin. Dub. Phil. M. J. Sc. 27, 184 (1864), 425--432.

[52]

J. S. Turner. 1957. Buoyant Vortex Rings. Proc. R. Soc. Lond. A 239, 1216 (1957), 61--75.

[53]

Hermann von Helmholtz. 1858. Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. J. Reine Angew. Math. 55 (1858), 25--55.

[54]

Steffen Weißmann and Ulrich Pinkall. 2010. Filament-based Smoke with Vortex Shedding and Variational Reconnection. ACM Trans. Graph. 29, 4 (2010), 115:1--12.

Digital Library

[55]

G. B. Whitham. 1974. Linear and Nonlinear Waves. Wiley.

[56]

Sheila E. Widnall and Donald B. Bliss. 1971. Slender-body Analysis of the Motion and Stability of a Vortex Filament Containing an Axial Flow. J. Fl. Mech. 50, 2 (1971), 335--353.

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On bubble rings and ink chandeliers

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 38, Issue 4

August 2019

1480 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3306346

Editor:
Olga Sorkine-Hornung
ETH Zurich

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Copyright © 2019 ACM.

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Publication History

Published: 12 July 2019

Published in TOG Volume 38, Issue 4

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Cited By

Wang SDeng YDeng MYu HZhou JChen DKomura TWu JZhu B(2024)An Eulerian Vortex Method on Flow MapsACM Transactions on Graphics10.1145/368799643:6(1-14)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687996
Li ZChen DLin CLiu JZhu B(2024)Particle-Laden Fluid on Flow MapsACM Transactions on Graphics10.1145/368791643:6(1-12)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687916
Chen JGain JChomaz JCani M(2024)TwisterForge: controllable and efficient animation of virtual tornadoesProceedings of the 17th ACM SIGGRAPH Conference on Motion, Interaction, and Games10.1145/3677388.3696335(1-11)Online publication date: 21-Nov-2024
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