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
tornado falls into this
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.
