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. The physics of vortex rings are still under active study in fluid dynamics. Devices have been invented which generate bubble vortex rings. Physics 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. 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: where is the growth rate, is the wave number, is the radius of the bubble cylinder, is the surface tension, is the circulation, and is the modified Bessel function of the second kind of order . When is positive, the bubble is stable due to circulation and when is negative, surface tension effects destabilize it and break it up. 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. 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