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Vortex created by the passage of an aircraft wing, revealed by
colored smoke
A vortex (plural: vortices) 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. The
speed and rate of rotation
of the fluid are greatest at the center, and decrease progressively
with distance from the center.
Properties
Vortices display some special properties:
- The fluid pressure in a vortex is lowest in the center (where
the speed is greatest) and rises progressively with distance from
the center. This is in accordance with Bernoulli's Principle. The core of a vortex
in air is sometimes visible because of a plume of water vapor
caused by condensation in the low pressure of the
core. The spout of a tornado
is a classic and frightening example of the visible core of a
vortex. A dust devil
is also the core of a vortex, made visible by the dust drawn
upwards by the turbulent flow of air from ground level into the low
pressure core.
- The core of every vortex can be considered to contain a vortex
line, and every particle in the vortex can be considered to be
circulating around the vortex line. Vortex lines can start and end
at the boundary of the fluid or form closed loops. They cannot
start or end in the fluid. (See Helmholtz's theorems.) Vortices
readily deflect and attach themselves to a solid surface. For
example, a vortex usually forms ahead of the propeller disk or jet engine of a slow-moving airplane. One end of the vortex
line is attached to the propeller disk or jet engine, but when the
airplane is taxiing the other end of the vortex line readily
attaches itself to the ground rather than end in midair. The vortex
can suck water and small stones into the core and then into the
propeller disk or jet engine.
- Two or more vortices that are approximately parallel and
circulating in the same direction will merge to form a single
vortex. The circulation of the merged
vortex will equal the sum of the circulations of the
constituent vortices. For example, a sheet of small vortices flows
from the trailing edge of the wing or propeller of an airplane when
the wing is developing lift or the propeller is developing thrust. In less than one wing chord
downstream of the trailing edge of the wing these small vortices
merge to form a single vortex. If viewed from the tail of the
airplane, looking forward in the direction of flight, there is one
wingtip
vortex trailing from the left-hand wing and circulating
clockwise, and another wingtip vortex trailing from the right-hand
wing and circulating anti-clockwise. The result is a region of
downwash behind the wing, between the pair of wingtip
vortices. These two wingtip vortices do not merge because
they are circulating in opposite directions.
- Vortices contain a lot of energy in the circular motion of the
fluid. In an ideal fluid this energy can never be dissipated and
the vortex would persist forever. However, real fluids exhibit viscosity and this
dissipates energy very slowly from the core of the vortex. (See Rankine vortex).
It is only through dissipation of a vortex due to viscosity that a
vortex line can end in the fluid, rather than at the boundary of
the fluid. For example, the wingtip vortices from an airplane
dissipate slowly and linger in the atmosphere long after the
airplane has passed. This is a hazard to other aircraft and is
known as wake
turbulence.
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, vorticity
is defined as the curl of the fluid velocity
:

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.
|
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 terms, the fluid near the center of the vortex
circulates faster than the fluid far from the center. 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.
Forced (rotational)
vortex
In a forced vortex the fluid essentially
rotates as a solid body (there is no shear). The motion can be
realized by placing a dish of fluid on a turntable rotating at ω
radians/sec; the fluid has vorticity of 2ω 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.
Vortices in
magnets
Different classes of vortex waves also exist in magnets. There
are exact solutions to classical nonlinear magnetic equations e.g.
Landau-Lifshitz equation, continuum Heisenberg
model, Ishimori equation, nonlinear Schrödinger
equation and so on.
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.
In atmospheric physics, 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.
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 which persists for a surprisingly long time,
illustrating the slow rate at which viscosity dissipates the energy
of a vortex.
- 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 the water would drain out, such as a
bathtub. A large, powerful whirlpool is known as a maelstrom. In popular
imagination, but only rarely in reality, can they have the
dangerous effect of destroying boats. Examples are Scylla and Charybdis of classical mythology in the Straits of Messina, Italy; the Naruto whirlpools
of Nankaido, Japan; the Maelstrom, Lofoten, Norway.
- 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. Earth's galaxy, the Milky Way, is of this
type.
See also
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
External
links