Тороидальные вихри в жидкости

Torus shaped vortex in a fluid

A vortex ring, also called a toroidal vortex, is a torus shaped vortex in a fluid; 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, in microbursts, and rarely in volcanic eruptions. 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.

In a typical vortex ring, the fluid particles move in roughly circular paths around an imaginary circle (the core) 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 (and hence most of the energy dissipation) 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.

The formation of vortex rings has fascinated the scientific community for more than a century, starting with William Barton Rogers who made sounding observations of the formation process of air vortex rings in air, air rings in liquids, and liquid rings in liquids. In particular, William Barton Rogers made use of the simple experimental method of letting a drop of liquid fall on a free liquid surface; a falling colored drop of liquid, such as milk or dyed water, will inevitably form a vortex ring at the interface due to the surface tension. A method proposed by G. I. Taylor to generate a vortex ring is to impulsively start a disk from rest. The flow separates to form a cylindrical vortex sheet and by artificially dissolving the disk, one is left with an isolated vortex ring. This is the case when someone is stirring their cup of coffee with a spoon and observing the propagation of a half vortex in the cup. In a laboratory, vortex rings are formed by impulsively discharging fluid through a sharp edged nozzle or orifice. The impulsive motion of the piston/cylinder system is either triggered by an electric actuator or by a pressurized vessel connected to a control valve. For a nozzle geometry, and at first approximation, the exhaust speed is uniform and equal to the piston speed. This is referred as a parallel starting jet. It is possible to have a conical nozzle in which the streamlines at the exhaust are directed toward the centerline. This is referred as a converging starting jet. The orifice geometry which consists in an orifice plate covering the straight tube exhaust, can be considered as an infinitely converging nozzle but the vortex formation differs considerably from the converging nozzle, principally due to the absence of boundary layer in the thickness of the orifice plate throughout the formation process. The fast moving fluid (A) is therefore discharged into a quiescent fluid (B). The shear imposed at the interface between the two fluids slows down the outer layer of the fluid (A) relatively to the centerline fluid. In order to satisfy the Kutta condition, the flow is forced to detach, curl and roll up in the form of a vortex sheet. Later, the vortex sheet detaches from the feeding jet and propagates freely downstream due to its self induced kinematics. This is the process commonly observed when a smoker forms smoke rings from their mouth, and how vortex ring toys work. Secondary effects are likely to modify the formation process of vortex rings. and jellyfishes or squids were shown to propel themselves in water by periodically discharging vortex rings in the surrounding. Finally, for more industrial applications, the synthetic jet which consists in periodically formed vortex rings, was proved to be an appealing technology for flow control, heat and mass transfer and thrust generation

Prior to Gharib et al. (1998), few studies had focused on the formation of vortex rings generated with long stroke to diameter ratios , where is the length of the column of fluid discharged through the exhaust and is the diameter of the exhaust. For short stroke ratios, only one isolated vortex ring is generated and no fluid is left behind in the formation process. For long stroke ratios, however, the vortex ring is followed by some energetic fluid, referred as the trailing jet. On top of showing experimental evidence of the phenomenon, an explanation of the phenomenon was provided in terms of energy maximisation invoking a variational principle first reported by Kelvin and later proven by Benjamin (1976), or Friedman & Turkington (1981). Ultimately, Gharib et al. (1998) For instance, it was shown that biological systems such as the human heart or swimming and flying animals generate vortex rings with a stroke to diameter ratio close to the formation number of about 4, hence giving ground to the existence of an optimal vortex ring formation process in terms of propulsion, thrust generation and mass transport. In particular, the squid lolliguncula brevis was shown to propel itself by periodically emitting vortex rings at a stroke ratio close to 4. and subsequently strengthened by analyses based on color Doppler mapping and magnetic resonance imaging. Some recent studies have also confirmed the presence of a vortex ring during rapid filling phase of diastole and implied that the process of vortex ring formation can influence mitral annulus dynamics.

Releasing air underwater forms bubble rings, which are vortex rings of water with bubbles (or even a single donut shaped bubble) trapped along its axis line. Such rings are often produced by scuba divers and dolphins.

There has been research and experiments on the existence of separated vortex rings (SVR) 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 symmetric SVR remains attached to the pappus for the duration of its flight and uses drag to enhance the travel. These dandelion seed structures have been used to create tiny battery free wireless sensors that can float in the wind and be dispersed across a large area.

The formation of vortex rings has fascinated the scientific community for more than a century, starting with William Barton Rogers who made sounding observations of the formation process of air vortex rings in air, air rings in liquids, and liquid rings in liquids. In particular, William Barton Rogers made use of the simple experimental method of letting a drop of liquid fall on a free liquid surface; a falling colored drop of liquid, such as milk or dyed water, will inevitably form a vortex ring at the interface due to the surface tension. 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.