Editing Bubble ring (section)

==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.
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<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.
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