Editing Bubble ring

{{Short description|Toroidal vortex ring of air in water}}
{{for|the bubble-blowing toy|Soap bubble#Use in play}}
[[File:Bubble Ring in Sunlight (cropped).jpg|thumb|upright=1.3|{{center|Bubble ring}}]]

A '''bubble ring''', or '''toroidal bubble''', is an underwater [[vortex ring]] where an air bubble occupies the core of the vortex, forming a ring shape. The ring of air as well as the nearby water spins [[Toroidal and poloidal|poloidally]] as it travels through the water, much like a flexible bracelet might spin when it is rolled on to a person's arm. The faster the bubble ring spins, the more stable it becomes.<ref>{{cite journal | last1 = Yoona | first1 = SS | last2 = Heister | first2 = SD  |author2-link=Stephen Douglas Heister | year = 2004 | title = A nonlinear atomization model based on a boundary layer instability mechanism | url = http://solarcellaerosol.korea.ac.kr/papers/paper-journal/ssyoon5_BLI_PoF2004.pdf | journal = Physics of Fluids | volume = 16 | issue = 1 | pages = 47–61 | doi = 10.1063/1.1629301 | bibcode = 2004PhFl...16...47Y | access-date = 2010-05-23 | archive-url = https://web.archive.org/web/20110722132615/http://solarcellaerosol.korea.ac.kr/papers/paper-journal/ssyoon5_BLI_PoF2004.pdf | archive-date = 2011-07-22 | url-status = dead }}</ref> The physics of vortex rings are still under active study in [[fluid dynamics]].<ref>{{cite journal | last1 = Ruban | first1 = VP | last2 = Rasmussen | first2 = JJ | year = 2003 | title = Toroidal bubbles with circulation in ideal hydrodynamics: A variational approach | journal = Phys. Rev. | volume = 68 | issue = 5| page = 5 | doi=10.1103/PhysRevE.68.056301| pmid = 14682878 |arxiv = physics/0306029 |bibcode = 2003PhRvE..68e6301R | s2cid = 11765709 }}</ref><ref>{{cite journal | last1 = Wang | first1 = QX | last2 = Yeo | first2 = KS | last3 = Khoo | first3 = BC | last4 = Lam | first4 = KY | year = 2005 | title = VORTEX ring modelling of toroidal bubbles | url = http://web.mat.bham.ac.uk/Q.X.Wang/papers_pdf/toroidal_bubble_wqx.pdf | journal = Theoretical and Computational Fluid Dynamics | volume = 19 | issue = 5| pages = 1432–2250 | doi=10.1007/s00162-005-0164-6|bibcode = 2005ThCFD..19..303W | s2cid = 52219528 }}</ref> Devices have been invented which generate bubble vortex rings.<ref>United States Patent: [http://www.google.co.nz/patents?hl=en&lr=&vid=USPAT7300040&id=O-KcAAAAEBAJ&oi=fnd&dq=%22ring+bubbles%22&printsec=abstract#v=onepage&q&f=false Simple method for the controlled production of VORTEX ring bubbles of a gas] {{Webarchive|url=https://web.archive.org/web/20110926205326/http://www.google.co.nz/patents?hl=en&lr=&vid=USPAT7300040&id=O-KcAAAAEBAJ&oi=fnd&dq=%22ring+bubbles%22&printsec=abstract#v=onepage&q&f=false |date=2011-09-26 }} Issued patent: 6824125, 30 November 2004.</ref><ref>United States Patent: [http://www.google.co.nz/patents?id=O-KcAAAAEBAJ&printsec=description&zoom=4#v=onepage&q&f=false Simple, mechanism-free device, and method to produce VORTEX ring bubbles in liquids] {{Webarchive|url=https://web.archive.org/web/20120224202432/http://www.google.co.nz/patents?id=O-KcAAAAEBAJ&printsec=description&zoom=4#v=onepage&q&f=false |date=2012-02-24 }} Patent number: 7300040. 27 November 2007.</ref>

==Physics==
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As the bubble ring rises, a lift force pointing downward that is generated by the vorticity acts on the bubble in order to counteract the buoyancy force. This reduces the bubble's velocity and increases its diameter. The ring becomes thinner, despite the total volume inside the bubble increasing as the external water pressure decreases.<ref>{{cite journal|last=Cheng|first=M. |author2=J. Lou |author3=T.T. Lim|title=Motion of a bubble ring in a viscous fluid|journal=Physics of Fluids|year=2013|volume=25|issue=6 |url=http://scitation.aip.org/docserver/fulltext/aip/journal/pof2/25/6/1.4811407.pdf?expires=1386197422&id=id&accname=freeContent&checksum=F7F77F63D0578CF01E3477EB897B8A08|access-date=15 October 2013|doi=10.1063/1.4811407|pages=067104–067104–19|bibcode = 2013PhFl...25f7104C }}</ref>  Bubble rings fragment into rings of spherical bubbles when the ring becomes thinner than a few millimetres. This is due to [[Plateau–Rayleigh instability]]. When the bubble reaches a certain thickness, surface tension effects distort the bubble's surface pulling it apart into separate bubbles. Circulation of the fluid around the bubble helps to stabilize the bubble for a longer duration, counteracting the effects of Plateau–Rayleigh instability. Below is the equation for Plateau–Rayleigh instability with circulation as a stabilizing term:

::<math> \omega^2= \left ( \frac{-ka \, K_1(ka)}{K_0(ka)} \right ) \left [ (1-k^2 a^2) \frac{T}{pa^3} - \frac{\Gamma^2}{4\pi^2 a^4} \right ] </math>

where <math>\omega</math> is the growth rate, <math>k</math> is the wave number, <math>a</math> is the radius of the bubble cylinder, <math>T</math> is the surface tension, <math>\Gamma</math> is the circulation, and <math>K_n(x)</math> is the [[modified Bessel function]] of the second kind of order <math>n</math>. When <math>\omega</math> is positive, the bubble is stable due to circulation and when <math>\omega</math> is negative, surface tension effects destabilize it and break it up.<ref>{{cite journal | last1 = Lundgren | first1 = TS | last2 = Mansour | first2 = NN | year = 1991 | title = VORTEX ring bubbles | journal = Journal of Fluid Mechanics | volume = 224 | pages = 177–196 | doi=10.1017/s0022112091001702|bibcode = 1991JFM...224..177L | s2cid = 120629247 | url = https://zenodo.org/record/1235805 }}</ref> Circulation also has an effect on the velocity and radial expansion of the bubble. Circulation increases the velocity while reducing the rate of radial expansion. Radial expansion however is what diffuses energy by stretching the vortex.<ref>{{cite journal|last=Cheng|first=M. |author2=J. Lou |author3=T.T. Lim|title=Motion of a bubble ring in a viscous fluid|journal=Physics of Fluids|year=2013|volume=25|issue=6 |url=http://scitation.aip.org/docserver/fulltext/aip/journal/pof2/25/6/1.4811407.pdf?expires=1386197422&id=id&accname=freeContent&checksum=F7F77F63D0578CF01E3477EB897B8A08|access-date=15 October 2013|doi=10.1063/1.4811407|pages=067104–067104–19|bibcode = 2013PhFl...25f7104C }}</ref> Instability happens more quickly in turbulent water, but in calm water, divers can achieve an external diameter of a meter or more before the bubble fragments.

===Buoyancy induced toroidal bubbles===
As an air bubble rises, there is a difference in pressure between the top and bottom of the bubble. The higher pressure at the bottom of the bubble pushes the bubble's bottom surface up faster than the top surface rises. This creates a fluid jet that moves up through the center of the bubble. If the fluid jet has enough energy, it will puncture the top of the bubble and create a bubble ring. Because of the motion of the fluid moving through the center of the bubble, the bubble begins to rotate. This rotation moves the fluid around the bubble creating a toroidal vortex. If the surface tension of the fluid interface or the viscosity of the liquid is too high, then the liquid jet will be more broad and will not penetrate the top of the bubble. This results in a spherical cap bubble.<ref>{{cite journal|last=Chen|first=Li|author2=Suresh V. Garimella|author3=John A. Reizes|author4=Eddie Leonardi|title=The development of a bubble rising in a viscous liquid|journal=Journal of Fluid Mechanics|year=1999|volume=387|issue=1|pages=61–96|doi=10.1017/s0022112099004449|bibcode = 1999JFM...387...61C |s2cid=18934972 }}<!--|accessdate=15 October 2013--></ref> Air bubbles with a diameter greater than about two centimeters become toroidal in shape due to the pressure differences.<ref>{{Cite journal |title=Ring Bubbles of Dolphins |author1=Ken Marten |author2=Karim Shariff |author3=Suchi Psarakos |author4=Don J. White |journal=Scientific American |volume=275 |issue=2 |pages=82–87 |url=http://www.sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=D0CD2470-180D-4C42-88B6-654E90AB55D |bibcode=1996SciAm.275b..82M |year=1996 |doi=10.1038/scientificamerican0896-82 |pmid=8693325 |access-date=2010-08-02 |archive-url=https://web.archive.org/web/20191218103217/http://www.sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=D0CD2470-180D-4C42-88B6-654E90AB55D |archive-date=2019-12-18 |url-status=dead |url-access=subscription }}.</ref>

===Cavitation bubbles===
[[Cavitation]] bubbles, when near a solid surface, can also become a torus. The area away from the surface has an increased static pressure causing a high pressure jet to develop. This jet is directed towards the solid surface and breaks through the bubble to form a torus shaped bubble for a short period of time. This generates multiple shock waves that can damage the surface.<ref>{{cite journal|last=Brujan|first=E.A.|author2=G.S. Keen|author3=A. Vogel|author4=J.R. Blake|title=The final stage of the collapse of a cavitation bubble close to a rigid boundary|journal=Physics of Fluids|date=January 2002|volume=14|issue=1|url=http://www.bmo.uni-luebeck.de/uploads/tx_wapublications/Brujan__2002_Physics_of_Fluids_The_final_stage_of_the_collapse_of_a_cavitation_bubble_close_to_a_rigid_boundary.pdf|access-date=21 October 2013|doi=10.1063/1.1421102|pages=85|bibcode=2002PhFl...14...85B|s2cid=13668310 |archive-url=https://web.archive.org/web/20160429211955/http://www.bmo.uni-luebeck.de/uploads/tx_wapublications/Brujan__2002_Physics_of_Fluids_The_final_stage_of_the_collapse_of_a_cavitation_bubble_close_to_a_rigid_boundary.pdf|archive-date=29 April 2016|url-status=dead}}</ref>

<gallery mode="packed" style="float:left" heights="120">
File:Vortex ring.gif|A bubble ring forms a [[vortex ring]], shaped like a doughnut which spins [[Toroidal and poloidal|poloidally]] in the direction of the arrows.
File:Bubble-ring-spin.png|The bubble ring travels in the same direction its innermost side rotates.
</gallery>

<gallery mode="packed" style="float:right" heights="160">
File:Nicobulle.JPG|An underwater diver blows a bubble ring.
File:Scuba diver produces a bubble ring 2018-03-07.jpg|A [[scuba diver]] blows a bubble ring.
</gallery>

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==Cetaceans==
[[Cetacean]]s, such as [[beluga whale]]s, [[dolphin]]s and [[humpback whale]]s, blow bubble rings. Dolphins sometimes engage in complex play behaviours, creating bubble rings on purpose, seemingly for amusement.<ref>{{cite web |url=http://www.deepocean.net/deepocean/index.php?science09.php |title=The physics of bubble rings and other diver's exhausts |access-date=2006-10-24 |url-status=dead |archive-url=https://web.archive.org/web/20061006163548/http://www.deepocean.net/deepocean/index.php?science09.php |archive-date=2006-10-06 }}</ref> There are two main methods of bubble ring production: rapid puffing of a burst of air into the water and allowing it to rise to the surface, forming a ring; or creating a toroidal vortex with their [[Fluke (tail)|flukes]] and injecting a bubble into the [[Helix|helical]] vortex currents thus formed. The dolphin will often then examine its creation visually and with sonar. They will sometimes play with the bubbles, distorting the bubble rings, breaking smaller bubble rings off of the original or splitting the original ring into two separate rings using their beak. They also appear to enjoy biting the vortex-rings they have created, so that they burst into many separate normal bubbles and then rise quickly to the surface. Dolphins also have the ability to form bubble rings with their flukes by using the reservoir of air at the surface.<ref>{{cite web |url=http://www.bubblerings.com/bubblerings/media.cfm |title=Bubble rings: Videos and Stills |access-date=2006-10-24 |url-status=dead |archive-url=https://web.archive.org/web/20061011195647/http://www.bubblerings.com/bubblerings/media.cfm |archive-date=2006-10-11 }}</ref>

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<gallery mode="packed" style="float:left" heights="180px">
File:Delphinapterus leucas Bubble Ring.JPG|[[Beluga whale]]s blowing bubble rings in [[Shimane Aquarium]]
File:Humpback-bubble-spiral Olson.jpg|Aerial view of a [[Humpback whale|humpback]] [[Humpback whale#Feeding and predators|bubble net]]
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Humpback whales use another type of bubble ring when they forage for fish. They surround a [[Shoaling and schooling|school]] of [[forage fish]] with a circular [[Humpback whale#Feeding and predators|bubble net]] and herd them into a [[bait ball]].<ref>{{cite news
|first=Deb
|last=Acklin
|title= Crittercam Reveals Secrets of the Marine World
|url=http://news.nationalgeographic.com/news/2002/06/0624_020624_TVbubble.html
|archive-url=https://web.archive.org/web/20020627064217/http://news.nationalgeographic.com/news/2002/06/0624_020624_TVbubble.html
|url-status=dead
|archive-date=June 27, 2002
|publisher= National Geographic News
|date=2005-08-05
|access-date=2007-11-01 }}</ref>

==Human divers==
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File:Soapbubbles-SteveEF.jpg| Boy blowing soap bubbles from a bubble ring
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Some [[scuba divers]] and [[free-diving|freedivers]] can create bubble rings by blowing air out of their mouth in a particular manner.  Long bubble rings also can form spontaneously in turbulent water such as heavy surf.

==Other uses of the term==
The term "bubble ring" is also used in other contexts. A common children's toy for blowing soap bubbles is called a bubble ring, and replaces the [[bubble pipe]] toy that was traditionally used for many years because the bubble pipe can be perceived as too reminiscent of smoking and therefore a bad example for children. Soapsuds are suspended on a ring connected by a stem to the screwcap of a bottle containing soapsuds.<ref>Erhard G (2006) [https://books.google.com/books?id=mesU4WbE5CIC&pg=PA277&dq=%22bubble+ring%22|%22bubble+rings%22&hl=en&ei=R835S7iKLtCXcb7o_eYL&sa=X&oi=book_result&ct=result&resnum=39&ved=0CNcBEOgBMCY#v=onepage&q=%22bubble%20ring%22|%22bubble%20rings%22&f=false ''Designing with plastics''] Page 227. Hanser Verlag. {{ISBN|978-1-56990-386-5}}</ref>

==See also==
* [[Carousel feeding]]
* [[Smoke ring]]
* [[Vortex ring toy]]

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==References==
{{Reflist|30em}}

==Further references==
* Das, D. and Kumar, V. (2005) "Experimental investigation of the trajectory of compressible vortex rings", 11th AIAA/CEAS Aeroacoustics Conference, page 2953. {{doi|10.2514/6.2005-2953}}.
* Hameroff SR, Kaszniak AW and Scott A (1998) [https://books.google.com/books?id=dliyExsqYGwC&pg=PA558&dq=%22bubble+ring%22|%22bubble+rings%22&hl=en&ei=R835S7iKLtCXcb7o_eYL&sa=X&oi=book_result&ct=result&resnum=10&ved=0CFgQ6AEwCQ#v=onepage&q=%22bubble%20ring%22|%22bubble%20rings%22&f=false ''Toward a science of consciousness II: the second Tucson discussions and debates''] Page 558. MIT Press. {{ISBN|978-0-262-08262-4}}.
* {{cite journal | last1 = Lundgren | first1 = TS | last2 = Mansour | first2 = NN | year = 1991 | title = Vortex ring bubbles | journal = Journal of Fluid Mechanics | volume = 224 | pages = 177–196 | doi=10.1017/s0022112091001702|bibcode = 1991JFM...224..177L | s2cid = 120629247 | url = https://zenodo.org/record/1235805 }}
* {{cite journal | last1 = Marten | first1 = K | last2 = Shariff | first2 = K | last3 = Psarakos | first3 = S | last4 = White | first4 = DJ | year = 1996 | title = Ring bubbles of dolphins. A number of bottlenose dolphins in Hawaii can create shimmering, stable rings and helices of air as part of play | journal = Scientific American | volume = 275 | issue = 2| pages = 82–87 | doi = 10.1038/scientificamerican0896-82 | pmid = 8693325 | bibcode = 1996SciAm.275b..82M }}
* {{cite journal | last1 = McCowan | first1 = B | last2 = Marino | first2 = L | last3 = Vance | first3 = E | last4 = Walke | first4 = L | last5 = Reiss | first5 = D | year = 2000 | title = Bubble Ring Play of Bottlenose Dolphins (Tursiops truncatus): Implications for Cognition | url = http://faculty.vetmed.ucdavis.edu/faculty/bjmccowan/Pubs/McCowanetal.JCP.2000.pdf | journal = Journal of Comparative Psychology | volume = 114 | issue = 1 | pages = 98–106 | doi = 10.1037/0735-7036.114.1.98 | pmid = 10739315 | access-date = 2010-05-23 | archive-date = 2010-06-10 | url-status = dead | archive-url = https://web.archive.org/web/20100610140808/http://faculty.vetmed.ucdavis.edu/faculty/bjmccowan/Pubs/McCowanetal.JCP.2000.pdf }}

== External links ==
{{Commons category|Bubble rings}}
* [https://web.archive.org/web/20051222180142/http://www.earthtrust.org/delringgallery.html Dolphin bubble rings]
* [https://www.youtube.com/watch?v=quiDUHNsq2E Dolphin make and play bubble rings (video)]
* [https://web.archive.org/web/20100528000815/http://www.bubblerings.com/bubblerings/media.cfm Various videos of bubble rings]

[[Category:Vortices]]