Vortex ring

# Vortex ring

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Encyclopedia
A vortex ring, also called a toroidal vortex, is a region of rotating fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

moving through the same or different fluid where the flow pattern takes on a toroid
Toroid (geometry)
In mathematics, a toroid is a doughnut-shaped object, such as an O-ring. Its annular shape is generated by revolving a plane geometrical figure about an axis external to that figure which is parallel to the plane of the figure and does not intersect the figure...

al (doughnut
Doughnut
A doughnut or donut is a fried dough food and is popular in many countries and prepared in various forms as a sweet snack that can be homemade or purchased in bakeries, supermarkets, food stalls, and franchised specialty outlets...

) shape. The movement of the fluid is about the poloidal or circular axis of the doughnut, in a twisting vortex
Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...

motion. Examples of this phenomenon are a smoke ring
Smoke ring
A smoke ring is a visible vortex ring formed by sudden release of smoke. It can be created by blowing smoke from the mouth, quickly lighting a cigarette lighter and putting it out or holding a burning incense stick or a cigarette vertically, pushing it with the burning side up and suddenly pulling...

or a microburst
Microburst
A microburst is a very localized column of sinking air, producing damaging divergent and straight-line winds at the surface that are similar to, but distinguishable from, tornadoes, which generally have convergent damage. There are two types of microbursts: wet microbursts and dry microbursts...

## Discovery

Vortex rings were first mathematically analysed by the German physicist Hermann von Helmholtz
Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...

, in his paper of 1867 On Integrals of the Hydrodynamical Equations which Express Vortex-motion.
Smoke rings have probably been observed since antiquity since they can easily be blown from the mouth.

## Vortex ring formation and structure

One way a vortex ring may be formed is by pushing a spherical mass of fast moving fluid (A) into a mass of stationary fluid (B). A and B may chemically be the same fluid. As B hits the ball of A it pushes the outer layers of A with it. The inner layers are less affected. The main mass of A forms a 'shadow' of lower pressure behind it, and the layer peeled off by B begins to curve round back into the main mass of A. This inward curving flow initiates the vortex, and splits it into a doughnut shape. Now B flows past both the inner and outer circumferences of the doughnut. The greater outer perimeter causes a net rolling the doughnut of A.

The leading edge of a plume
Plume (hydrodynamics)
In hydrodynamics, a plume is a column of one fluid or gas moving through another. Several effects control the motion of the fluid, including momentum, diffusion, and buoyancy...

, sometimes called the 'starting-plume', usually has a vortex-ring structure, as does a smoke ring
Smoke ring
A smoke ring is a visible vortex ring formed by sudden release of smoke. It can be created by blowing smoke from the mouth, quickly lighting a cigarette lighter and putting it out or holding a burning incense stick or a cigarette vertically, pushing it with the burning side up and suddenly pulling...

. The motion of an isolated vortex ring and the interaction of two or more vortices are discussed in eg Batchelor
George Batchelor
George Keith Batchelor FRS was an Australian applied mathematician and fluid dynamicist. He was for many years the Professor of Applied Mathematics in the University of Cambridge, and was founding head of the Department of Applied Mathematics and Theoretical Physics...

's text book.

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, is known in which the vorticity is distributed within a sphere (the internal symmetry of the flow is however still annular). Such a structure or an electromagnetic equivalent has been suggested as an explanation for the internal structure of ball lightning
Ball lightning
Ball lightning is an unexplained atmospheric electrical phenomenon. The term refers to reports of luminous, usually spherical objects which vary from pea-sized to several metres in diameter. It is usually associated with thunderstorms, but lasts considerably longer than the split-second flash of a...

. For example, Shafranov used a magnetohydrodynamic (MHD) 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.

## Vortex ring effect in helicopters

Vortex ring state (VRS), also known as settling with power, is a hazardous condition encountered in helicopter flight. It happens when three things occur during flight: A high rate of descent, an airspeed lower than effective translational lift
Translational lift
Translational lift is a transitional state present as a helicopter moves from hover to forward flight...

, and when the helicopter is using a large portion of its available power. A helicopter's main rotor typically directs airflow downwards to create lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

, but with low horizontal airspeed, it induces a vortex ring. A toroid
Toroid
Toroid may refer to*Toroid , a doughnut-like solid whose surface is a torus.*Toroidal inductors and transformers which have wire windings on circular ring shaped magnetic cores.*Vortex ring, a toroidal flow in fluid mechanics....

-shaped path of airflow circumscribes the blade disc, as the airflow moves down through the disc, then outward, up, inward, and then down through the top again. This re-circulation of flow can negate much of the lifting force and cause a catastrophic loss of altitude. Specific to vortex ring state is that the helicopter, operating in its own downwash
Downwash
In aeronautics downwash is the air forced down by the aerodynamic action of a wing or helicopter rotor blade in motion, as part of the process of producing lift....

, is descending through descending air. Applying more power (increasing collective pitch) serves to further accelerate the downwash through which the main-rotor is descending, exacerbating the condition.

In single rotor helicopters, a VRS can be corrected by moving the cyclic forward, which controls the pitch angle of the rotor blade, slightly pitching nose down, and establishing forward flight. In tandem-rotor helicopters, recovery is accomplished through lateral cyclic or pedal input. The aircraft will fly into "clean air", and will be able to regain lift.

## Vortex ring in the left ventricle of the heart

One of the most important fluid phenomena observed in the left ventricle during cardiac relaxation (diastole
Diastole
Diastole is the period of time when the heart fills with blood after systole . Ventricular diastole is the period during which the ventricles are relaxing, while atrial diastole is the period during which the atria are relaxing...

) is the vortex ring that develops with a strong jet
Jet (fluid)
A jet is an efflux of fluid that is projected into a surrounding medium, usually from some kind of a nozzle, aperture or orifice. Jets can travel long distances without dissipating...

entering through the mitral valve
Mitral valve
The mitral valve is a dual-flap valve in the heart that lies between the left atrium and the left ventricle...

. The presence of these flow structures that develop during cardiac diastole
Diastole
Diastole is the period of time when the heart fills with blood after systole . Ventricular diastole is the period during which the ventricles are relaxing, while atrial diastole is the period during which the atria are relaxing...

was initially recognized by in-vitro visualization of the ventricular flow and subsequently strengthened by analyses based on color Doppler mapping and Magnetic Resonance Imaging
Magnetic resonance imaging
Magnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...

. Some recent studies have also confirmed the presence of a vortex ring during rapid filling phase of diastole
Diastole
Diastole is the period of time when the heart fills with blood after systole . Ventricular diastole is the period during which the ventricles are relaxing, while atrial diastole is the period during which the atria are relaxing...

and implied that the process of vortex ring formation can influence on mitral annulus
Mitral annulus
The mitral annulus is a fibrous ring that is attached to the mitral valve leaflets. Unlike prosthetic valves, it is neither circular nor continuous. The annulus contracts and reduces its surface area during systole to help provide complete closure of the leaflets. Annular dilatation can result in...

dynamics.

## Instability

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 (stretched in the horizontal direction and squeezed in the vertical) before reversing the process and returning to the original state.

• Aeronautical engineering
• Air bazooka
Air bazooka
The air vortex cannon, sold commercially as the air bazooka or airzooka is a short, wide plastic tube with a slight taper and a plastic diaphragm at the larger end. The diaphragm is attached to elastic strips which allow it to be extended and released with a sudden rush forcing a quantity of air...

• Autorotation
Autorotation
In aviation, autorotation refers to processes in both fixed-wing and rotary-wing aircraft. The term means significantly different things in each context....

• Bubble ring
Bubble ring
A bubble ring, or ring bubble, is an underwater ring vortex 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...

• Ground effect in aircraft
• Helicopter flight controls
Helicopter flight controls
A helicopter pilot manipulates the helicopter flight controls in order to achieve controlled aerodynamic flight. The changes made to the flight controls are transmitted mechanically to the rotor, producing aerodynamic effects on the helicopter's rotor blades which allow the helicopter to be...

• Helicopter pilotage
• Helicopter rotor
Helicopter rotor
A helicopter main rotor or rotor system is a type of fan that is used to generate both the aerodynamic lift force that supports the weight of the helicopter, and thrust which counteracts aerodynamic drag in forward flight...

• Mushroom cloud
Mushroom cloud
A mushroom cloud is a distinctive pyrocumulus mushroom-shaped cloud of condensed water vapor or debris resulting from a very large explosion. They are most commonly associated with nuclear explosions, but any sufficiently large blast will produce the same sort of effect. They can be caused by...

• Smoke ring
Smoke ring
A smoke ring is a visible vortex ring formed by sudden release of smoke. It can be created by blowing smoke from the mouth, quickly lighting a cigarette lighter and putting it out or holding a burning incense stick or a cigarette vertically, pushing it with the burning side up and suddenly pulling...

• Vortex ring gun
Vortex ring gun
The vortex ring gun is an experimental non-lethal weapon in which a blank cartridge is fired into a gun barrel that has a diverging nozzle screwed onto the muzzle...

• Vortex ring toys
Vortex ring toys
A vortex ring toy generates vortex rings – rolling donut-shapes of fluid – that move through the fluid . A smoke ring is a common example of a vortex ring...