Vortex

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Vortex created by the passage of an aircraft wing, revealed by coloured smoke

A vortex (pl. vortices) is a spinning, often turbulent, flow (or any spiral motion) with closed streamlines. The shape of media or mass swirling rapidly around a center forms a vortex. It flows in a circular motion.

[edit] Dynamics

A vortex can be any circular or rotary flow that possesses vorticity. Vorticity is a mathematical concept used in fluid dynamics. It can be related to the amount of "circulation" or "rotation" in a fluid. In fluid dynamics, vorticity is the circulation per unit area at a point in the flow field. It is a vector quantity, whose direction is (roughly speaking) along the axis of the swirl. Also in fluid dynamics, the movement of a fluid can be said to be vortical if the fluid moves around in a circle, or in a helix, or if it tends to spin around some axis. Such motion can also be called solenoidal. In the atmospheric sciences, vorticity is a property that characterizes large-scale rotation of air masses. Since the atmospheric circulation is nearly horizontal, the (3 dimensional) vorticity is nearly vertical, and it is common to use the vertical component as a scalar vorticity.

Mathematically, it is defined as,

where is the fluid velocity.

The properties of vorticity in 2 and 3 dimensions are treated in some depth in George Batchelor's famous textbook (ch 5 & ch 7 et seq.). Of particular importance in practical situations is the intensification of vorticity which takes place in three dimensions when a vortex-line is extended (p270 et seq).

[edit] Two types of vortex

In fluid mechanics, a distinction is often made between two limiting vortex cases. One is called the free (irrotational) vortex, and the other is the forced (rotational) vortex. These are considered as below:

Two autumn leaves in a counter-clockwise vortex (reference position).

Two autumn leaves in a rotational vortex rotate with the counter-clockwise flow.

Two autumn leaves in an irrotational vortex preserve their original orientation while moving counter-clockwise.

[edit] Free (irrotational) vortex

When fluid is drawn down a plug-hole, one can observe the phenomenon of a free vortex. The tangential velocity v varies inversely as the distance r from the center of rotation, so the angular momentum, rv, is constant; the vorticity is zero everywhere (except for a singularity at the center-line) and the circulation about a contour containing r=0 has the same value everywhere. The free surface (if present) dips sharply (as r ^{− 2} ) as the center line is approached.

The tangential velocity is given by:

                 (2.1)

where Γ is the circulation and r is the radial distance from the center of the vortex.

In non technical lingo, the circular streamlines toward the center can sweep out a given angle faster than the outer streamlines. The speed along the circular path of flow is held constant or decreases as you move out from the center. At the same time the inner streamlines have a shorter distance to travel to complete a ring. If you were running a race on a circular track would you rather be on the inside or outside, assuming the goal was to complete a circle? Imagine a leaf floating in a free vortex. The leaf's tip points to the center and the blade straddles multiple streamlines. The outer flow is slow in terms of angle traversed and it exerts a backwards tug on the base of the leaf while the faster inner flow pulls the tip forwards. The drag force opposes rotation of the leaf as it moves around the circle.

[edit] Forced (rotational) vortex

In a forced vortex the fluid essentially rotates as a solid body (there is no shear). The motion can be realised by placing a dish of fluid on a turntable rotating at T radians/sec; the fluid has vorticity of 2 T everywhere, and the free surface (if present) is a parabola.

The tangential velocity is given by:

                 (2.2)

where ω is the angular velocity and r is the radial distance from the center of the vortex.

[edit] Observations

A vortex can be seen in the spiraling motion of air or liquid around a center of rotation. Circular current of water of conflicting tides form vortex shapes. Turbulent flow makes many vortices. A good example of a vortex is the atmospheric phenomenon of a whirlwind or a tornado or dust devil. This whirling air mass mostly takes the form of a helix, column, or spiral. Tornadoes develop from severe thunderstorms, usually spawned from squall lines and supercell thunderstorms, though they sometimes happen as a result of a hurricane.

A mesovortex is on the scale of a few miles (smaller than a hurricane but larger than a tornado). _[2] On a much smaller scale, a vortex is usually formed as water goes down a drain, as in a sink or a toilet. This occurs in water as the revolving mass forms a whirlpool. This whirlpool is caused by water flowing out of a small opening in the bottom of a basin or reservoir. This swirling flow structure within a region of fluid flow opens downward from the water surface.

[edit] Instances

• In the hydrodynamic interpretation of the behaviour of electromagnetic fields, the acceleration of electric fluid in a particular direction creates a positive vortex of magnetic fluid. This in turn creates around itself a corresponding negative vortex of electric fluid.
• Smoke ring : A ring of smoke in the air.
• Lift-induced drag of a wing on an aircraft.
• The primary cause of drag in the sail of a sloop.
• Whirlpool : a swirling body of water produced by ocean tides or by a hole underneath the vortex, where water drains out, as in a bathtub. In popular imagination, but only rarely in reality, can they have the dangerous effect of destroying boats.^{[citation needed]}
• Tornado : a violent windstorm characterized by a twisting, funnel-shaped cloud. A less violent version of a tornado, over water, is called a waterspout.
• Hurricane : a much larger, swirling body of clouds produced by evaporating warm ocean water and influenced by the Earth's rotation. Similar, but far greater, vortices are also seen on other planets, such as the permanent Great Red Spot on Jupiter and the intermittent Great Dark Spot on Neptune.
• Polar vortex : a persistent, large-scale cyclone centered near the Earth's poles, in the middle and upper troposphere and the stratosphere.
• Sunspot : dark region on the Sun's surface (photosphere) marked by a lower temperature than its surroundings, and intense magnetic activity.
• The accretion disk of a black hole or other massive gravitational source.
• Spiral galaxy : a type of galaxy in the Hubble sequence which is characterized by a thin, rotating disk. Our galaxy, the Milky Way is of this type.

[edit] See also

• Cyclonic separation
• Eddy
• Fan death
• Oregon Vortex
• Optical Vortex
• Viktor Schauberger
• Shower-curtain effect
• Spiral
• Strouhal number
• Vile Vortices
• Von Kármán vortex street
• Vortex ring
• Vortex tube
• Vortex cooler
• Vortex shedding
• Wingtip vortices
• Quantum vortex

[edit] References and further reading

• "Weather Glossary"' The Weather Channel Interactive, Inc.. 2004.
• "Glossary and Abbreviations". Risk Prediction Initiative. The Bermuda Biological Station for Research, Inc.. St. George's, Bermuda. 2004.
• Loper, David E., "An analysis of confined magnetohydrodynamic vortex flows". Case Institute of Technology. Washington, National Aeronautics and Space Administration]; for sale by the Clearinghouse for Federal Scientific and Technical Information, Springfield, Va. 1966. (NASA contractor report NASA CR-646) LCCN 67060315
• Batchelor, G. K. (1967), An Introduction to Fluid Dynamics, Cambridge Univ. Press, Ch. 7 et seq.

[edit] External links

• Dust Devil Movie A short movie showing many spinning vortices of varying sizes
• Video of two water vortex rings colliding (MPEG)
• BubbleRings.com Web site on "bubble rings", which are underwater rings made of air formed from vortices. The site has some information on how these rings work.
• Chapter 3 Rotational Flows: Circulation and Turbulence