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Vortex

Encyclopedia : V : VO : VOR : Vortex

For other uses, see Vortex (disambiguation)}}}.
Vortex created by the passage of an aircraft wing, revealed by coloured smoke
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Vortex created by the passage of an aircraft wing, revealed by coloured smoke

A vortex is a spinning, often turbulent, flow (or any spiral motion) with closed streamlines. The shape of media or mass rotating rapidly around a center forms a vortex. It is a flow involving rotation about an axis.

Contents

Dynamics

A vortex can be any circular or rotary flow that possesses vorticity.[1] 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 = \nabla \times \mathit]
where [\mathit=\mathrm\mathit + \mathrm\mathit + \mathrm\mathit] 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^] ) as the centre line is approached.

The tangential velocity is given by:

[v_ = \frac\,]                 (2.1)
where Γ is the circulation 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_ = \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 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.

Instances

See also

Water vortex
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Water vortex

References and further reading

External links

 

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