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Vortex & vorticity

When we describe some occurrences or events in nature, often we need to describe a momentary state of an atmospheric fluid. Vorticity is among the ‘state variables’ like temperature, density, pressure, velocity etc, which are commonly used to describe a fluid motion. So to understand the dynamics of tornado, we should have some idea about what ‘vorticity’ is.

Vorticity

Vorticity can be defined as “the angular velocity of matter  at a point in continuum space” [Ref: Lugt (1983)].In a fluid flow, vorticity is a measure of the local rotation and mathematically:

Vorticity = Curl(Velocity vector)

That means, a flow becomes ‘irrotational’ if there are no local rotations in the fluid flow.

Vortex

The definition of vortex is not very simple. In one way we can call it as the region in a fluid where vorticity is higher compared to the surrounding.

Disklike vortex: for a vortex, if the diameter is much larger than the axial scale it is a ‘disk-like’ vortex. Hurricane is one example of this type of vortex.

http://hurricanes.noaa.gov/images

Columnar Vortex: On the
other hand if the diameter
is much smaller than the
axial scale – it is called
‘columnar’ vortex. A
category.

http://www.spc.noaa.gov

In general, we can say, when there is a vortex, it has some vorticity. But,the reverse is not necessarily true. With all vorticities, there may not be a vortex attached. A parallel shear flow, which is not a vortex, has vorticity too.

Vortices are of different dimensions. Example  of one such extremely small vortex is "quantized votex"  in liquid helium (diameter ~ 10-10 m). Extermely large vortices are the Galaxies, diameters of which are of the order of light-years.

Vortices behind the falling leaves are of  the order of 1cm. Dust devils are larger cousins (~ 1m - 10m) to these small vortices.

Tornadoes or waterspouts are much larger vortices  with much larger diameter ( 100m – 1000m).

The following examples are in order of growing diameter: hurricanes, ocean circulations, great red spot of Jupiter.

Tapas Bhattacharya
Web-project :  Phys-645, Fall-2007, UAF.
Animation for 'Home'  - taken from .

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