# Bubble ring

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 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.[1] Bubble rings and smoke rings are both examples of vortex rings—the physics of which is still under active study in fluid dynamics.[2][3] Devices have been invented which generate bubble vortex rings.[4][5]

## Physics

 Dolphin play bubble rings SeaWorld Extraordinary toroidal vortices YouTube[6] Bubble ring Time warp - In slow motion YouTube

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.[7] 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:

$\omega^2= \left ( \frac{kaK_1}{ka} \right ) \left [ (1-k^2 a^2) \frac{T}{pa^3} - \frac{\Gamma^2}{4\pi^2 a^4} \right ]$

where ω is the growth rate, k is the wave number, a is the radius of the bubble cylinder, T is the surface tension, Γ is the circulation, and K0 and K1 are Bessel functions. When ω is positive the bubble is stable due to circulation and when ω is negative, surface tension effects destabilize it and break it up.[8] 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.[9] Instability happens more quickly in turbulent water, but in calm water divers can achieve an external diameter of a metre 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.[10] Air bubbles with a diameter greater than about two centimeters become toroidal in shape due to the pressure differences.[11]

### 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.[12]

## Cetaceans

Cetaceans, such as beluga whales, dolphins and humpback whales, blow bubble rings. Dolphins sometimes engage in complex play behaviours, creating bubble rings on purpose, seemingly for amusement.[13] 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 flukes and injecting a bubble into the 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've 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.[14]

Humpback whales use another type of bubble ring when they forage for fish. They surround a school of forage fish with a circular bubble net and herd them into a bait ball.[15]

## Human divers

Boy blowing soap bubbles from a bubble ring

Some scuba divers and 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.[16]

## References

1. ^ Yoona SS and Heister SD (2004) "A nonlinear atomization model based on a boundary layer instability mechanism" Physics of Fluids, 16 (1): 47–61.
2. ^ Ruban VP and Rasmussen JJ (2003) "Toroidal bubbles with circulation in ideal hydrodynamics: A variational approach" Phys. Rev, 68 (5).
3. ^ Wang QX, Yeo KS, Khoo BC and Lam KY (2005) "Vortex ring modelling of toroidal bubbles" JournalTheoretical and Computational Fluid Dynamics, 19 (5): 1432-2250.
4. ^ United States Patent: Simple method for the controlled production of vortex ring bubbles of a gas Issued patent: 6824125, 30 November 2004.
5. ^ United States Patent: Simple, mechanism-free device, and method to produce vortex ring bubbles in liquids Patent number: 7300040. 27 November 2007.
6. ^ Note that although a number of YouTube videos refer to bubble rings as toroidal vortices, they are in fact poloidal vortices
7. ^ Cheng, M.; J. Lou, T.T. Lim (2013). "Motion of a bubble ring in a viscous fluid" (PDF). Physics of Fluids 25. Retrieved 15 October 2013.
8. ^ Lundgren TS and Mansour NN (1991) "Vortex ring bubbles" Journal of Fluid Mechanics, 224:177-196.
9. ^ Cheng, M.; J. Lou, T.T. Lim (2013). "Motion of a bubble ring in a viscous fluid" (PDF). Physics of Fluids 25. Retrieved 15 October 2013.
10. ^ Chen, Li; Suresh V. Garimella; John A. Reizes; Eddie Leonardi (1999). "The development of a bubble rising in a viscous liquid". Journal of Fluid Mechanics 387: 61–96. doi:10.1017/s0022112099004449.
11. ^ Ken Marten; Karim Shariff; Suchi Psarakos; Don J. White. "Ring Bubbles of Dolphins". Scientific American..
12. ^ Brujan, E.A.; G.S. Keen, A. Vogel, J.R. Blake (January 2002). "The final stage of the collapse of a cavitation bubble close to a rigid boundary" (PDF). Physics of Fluids 14 (1). Retrieved 21 October 2013.
13. ^ "The physics of bubble rings and other diver's exhausts". Retrieved 2006-10-24.
14. ^ "Bubble rings: Videos and Stills". Retrieved 2006-10-24.
15. ^ Acklin, Deb (2005-08-05). "Crittercam Reveals Secrets of the Marine World". National Geographic News. Retrieved 2007-11-01.
16. ^ Erhard G (2006) Designing with plastics Page 227. Hanser Verlag. ISBN 978-1-56990-386-5