Vortices

A vortex is a spinning, often Turbulent , flow (or any Spiral motion) with closed Streamline s. The shape of media or mass rotating rapidly around a center forms a vortex. It is a flow involving rotation about an axis (vertical or horizontal).

DYNAMICS

A vortex can be any circular or rotary flow that possesses '' Vorticity ''._{{Link without Title}} 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,

::

\omega = 
abla 	imes \mathit{u}

where

\mathit{u}=\mathrm{u}\mathit{i} + \mathrm{v}\mathit{j} + \mathrm{w}\mathit{k}

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).

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:

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 centre of rotation, so the angular momentum, rv, is constant; the vorticity is zero everywhere (except for a singularity at the centre-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 centre line is approached.

The tangential velocity is given by:

:

v_{r} = rac{\Gamma}{2 \pi r}\,

(2.1)

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

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:

:

v_{r} = \omega r\,

(2.2)

where ω is the Angular Velocity and r is the radial distance from the center of the vortex.

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 Tide s 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 Line s and Supercell Thunderstorm s, though they sometimes happen as a result of a Hurricane .

A ''mesovortex'' is on the scale of a few Mile s (smaller than a hurricane but larger than a tornado). _{{Link without Title}} 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 Field s, 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.

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.

is of this type.

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Vortices