A vortex ring, also called a toroidal vortex, is a torus-shaped vortex in a fluid or gas; that is, a region where the fluid mostly spins around an imaginary axis line that forms a closed loop. The dominant flow in a vortex ring is said to be toroidal, more precisely poloidal. Vortex rings are plentiful in turbulent flows of liquids and gases, but are rarely noticed unless the motion of the fluid is revealed by suspended particles—as in the smoke rings which are often produced intentionally or accidentally by smokers. Fiery vortex rings are also a commonly produced trick by fire eaters. Visible vortex rings can also be formed by the firing of certain artillery, in mushroom clouds, and in microbursts. A vortex ring usually tends to move in a direction that is perpendicular to the plane of the ring and such that the inner edge of the ring moves faster forward than the outer edge. Within a stationary body of fluid, a vortex ring can travel for relatively long distance, carrying the spinning fluid with it.
Structure
In a typical vortex ring, the fluid particles move in roughly circular paths around an imaginary circle that is perpendicular to those paths. As in any vortex, the velocity of the fluid is roughly constant except near the core, so that the angular velocity increases towards the core, and most of the vorticity is concentrated near it. Unlike a sea wave, whose motion is only apparent, a moving vortex ring actually carries the spinning fluid along. Just as a rotating wheel lessens friction between a car and the ground, the poloidal flow of the vortex lessens the friction between the core and the surrounding stationary fluid, allowing it to travel a long distance with relatively little loss of mass and kinetic energy, and little change in size or shape. Thus, a vortex ring can carry mass much further and with less dispersion than a jet of fluid. That explains, for instance, why a smoke ring keeps traveling long after any extra smoke blown out with it has stopped and dispersed. These properties of vortex rings are exploited in the vortex ring gun for riot control and vortex ring toys such as the air vortex cannons.
Formation
One way a vortex ring may be formed is by injecting a compact mass of fast moving fluid into a mass of stationary fluid . Viscous friction at the interface between the two fluids slows down the outer layers of A relative to its core. Those outer layers then slip around the mass A and collect at the rear, where they re-enter the mass in the wake of the faster-moving inner part. The net result is a poloidal flow in A that evolves into a vortex ring. This mechanism is commonly seen, for example, when a drop of colored liquid falls into a cup of water. It is also often seen at the leading edge of a plume or jet of fluid as it enters a stationary mass; the mushroom-like head that develops at the tip of the jet has a vortex-ring structure. A variant of this process may occur when a jet within a fluid hits a flat surface, as in a microburst. In this case the poloidal spinning of the vortex ring is due to viscous friction between the layer of fast outward flow near the surface and the slower-moving fluid above it. A vortex ring is also formed when a mass of fluid is impulsively pushed from an enclosed space through a narrow opening. In this case the poloidal flow is set in motion, at least in part, by interaction between the outer parts of the fluid mass and the edges of the opening. This is how a smoker expels smoke rings from the mouth, and how most vortex ring toys work. Vortex rings may also be formed in the wake of a solid object that falls or moves through a fluid at sufficient speed. They may form also ahead of an object that abruptly reverses its motion with the fluid, as when producing smoke rings by shaking an incense stick. A vortex ring can also be created by a spinning propeller, as in a blender.
Air vortices can form around the main rotor of a helicopter, causing a dangerous condition known as vortex ring state or "settling with power". In this condition, air that moves down through the rotor turns outward, then up, inward, and then down through the rotor again. This re-circulation of flow can negate much of the lifting force and cause a catastrophic loss of altitude. Applying more power serves to further accelerate the downwash through which the main-rotor is descending, exacerbating the condition.
Releasing air underwater forms bubble rings, which are vortex rings of water with bubbles trapped along its axis line. Such rings are often produced by scuba divers and dolphins.
Separated Vortex Rings
There has been research and experiments on the existence of separated vortex rings such as those formed in the wake of the pappus of a dandelion. This special type of vortex ring effectively stabilizes the seed as it travels through the air and increases the lift generated by the seed. Compared to a standard vortex ring, which is propelled downstream, the axially symettric SVR remains attached to the pappus for the duration of its flight and uses drag to enhance the travel.
Theory
Historical studies
Vortex rings must have been known for as long as people have been smoking, but a scientific understanding of their nature had to wait for the development of mathematical models of fluid dynamics, such as the Navier-Stokes equations. Vortex rings were first mathematically analyzed by the German physicist Hermann von Helmholtz, in his 1858 paper On Integrals of the Hydrodynamical Equations which Express Vortex-motion. The formation, motion and interaction of vortex rings have been extensively studied.
Spherical vortices
For many purposes a ring vortex may be approximated as having a vortex-core of small cross-section. However a simple theoretical solution, called Hill's spherical vortex after the English mathematician Micaiah John Muller Hill, is known in which the vorticity is distributed within a sphere. Such a structure or an electromagnetic equivalent has been suggested as an explanation for the internal structure of ball lightning. For example, Shafranov used a magnetohydrodynamic analogy to Hill's stationary fluid mechanical vortex to consider the equilibrium conditions of axially symmetric MHD configurations, reducing the problem to the theory of stationary flow of an incompressible fluid. In axial symmetry, he considered general equilibrium for distributed currents and concluded under the Virial Theorem that if there were no gravitation, a bounded equilibrium configuration could exist only in the presence of an azimuthal current.
Instabilities
A kind of azimuthal radiant-symmetric structure was observed by Maxworthy when the vortex ring traveled around a critical velocity, which is between the turbulence and laminar states. Later Huang and Chan reported that if the initial state of the vortex ring is not perfectly circular, another kind of instability would occur. An elliptical vortex ring undergoes an oscillation in which it is first stretched in the vertical direction and squeezed in the horizontal direction, then passes through an intermediate state where it is circular, then is deformed in the opposite way before reversing the process and returning to the original state.
