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Tropical revolving storms.

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What they are
A tropical storm is an intense low pressure weather system, that can last for days to weeks within the Tropical regions of our planet.  They are tropical revolving storms because they are spun on their journey by the Coriolis force of the Earths spin. 
The Earth is 40,000 kilometers (24,900 miles) around at its widest part, the equator. Because it spins on its axis once in 24 hours, a point on the Earth's equator is traveling about 1,700 km per hour (1,000 miles per hour) relative to its axis. But the closer you get to the poles, the smaller the track a point takes in its daily rotation. At 60 North or South latitude, the track is only half the distance that it is at the equator, and so a point travels only half as fast. Air (or water) moving from high latitudes to low then tends to lag, and a person on the surface would feel a wind blowing out of the east. On the other hand, air moving from low latitudes to high is deflected westwards. This also means that moving air or water is deflected to the right in the northern hemisphere, and to the left in the southern hemisphere.  It is this deflection that causes tropical storms to rotate.

Where they occur

Tropical storms are known by many names, including hurricanes (North America), cyclones (India) and typhoons (Japan and East Asia).  They all occur in a band that lies roughly between the tropics of Cancer and Capricorn and despite varying wind speeds are ferocious storms. Some storms can form just outside of the tropics, but in general the distribution (location) of these storms is controlled by the places where sea temperatures rise above 27C and is heated to a sufficient depth.

The highest number of storms does not occur in the Atlantic close to the USA, but in the North Pacific affecting countries such as the Philippines and Japan. This is despite the fact that in the UK we only really get to hear about tropical storms affecting the USA. The most affected area being South East Asia receives an average of 26 storms per year. The least affected area is India where there is an average of 2 tropical storms per year.
Tropical storm track map

The Saffir-Simpson scale

Tropical storms are defined by their wind speeds and the potential damage they can cause, using what is known as the Saffir Simpson scale. Many tropical storms form between the tropics, some develop into tropical depressions but not many actually develop into full blown hurricanes/cyclones/typhoons.  As the sea temperature increases uplift of air increases and pressure decreases.  The Saffir Simpson also accounts for the height of the storm surge, the huge waves of water that are whipped up by the storms.
The Saffir-Simpson scale for Hurricane classification

Wind speeds are used to decide what category of storm a tropical storm is, over 120Kph or 74 mile per hour is needed for a category 1 hurricane, Over 250Kph or 149 miles per hour is the worst hurricane, a category 5 which would cause extreme damage.  Watch an animation of the Saffir-Simpson scale in action.

How Tropical storms form:

Diagram showing the structure of a hurricane

Tropical storms form whenever sea temperatures rise above 27 C and can be up to 650km across. They occur where the trade winds converge and often when the ITCZ has migrated to its most Northerly extent allowing air to converge or come together at low levels.   The suns heat passes through our atmosphere and warms the ocean water throughout the summer.  The sea is constantly moving and heat is redistributed to deeper parts of the ocean so this takes quite some time (this is why hurricanes occur in late summer - when sea temperature is at its highest).
This causes the seas temperature to rise to 27C and above, which encourages evaporation and the rising of air and water vapour up through the atmosphere in thermals (find out more from USA Today.com).
As these thermals rise the temperature drops (at 9.7C per 1000m ascent or the DALR).  Progressively the relative humidity rises as the air ascends (as cooler air can hold less water vapour than warmer air), eventually this causes the water vapour to condense into tiny droplets around dust and pollen (condensation nuclei).  These droplets collide together to form bigger droplets and thus helps to form huge cumulonimbus clouds. Latent heat is released during condensation fuelling the storm further. Eventually these droplets will collide and coalesce with one another, become bigger and fall as rain. As a result of condensation, latent heat is released and te air cools at a slower rate, the SALR, this fuels the storm further.
Because the air has risen in the centre of this storm, an area of low atmospheric pressure exists at the surface.  The Earth's atmosphere acts to balance this out as air rushes from surrounding high pressure areas to the centre of the storm along the pressure gradient.  This creates the high winds in the storm, and the lower the pressure gets in the centre of the storm relative to the pressure surrounding the storm, the stronger the winds will become as the pressure gradient steepens.
The whole storm slowly migrates across oceans towards land, and because of the Earths rotation or spin (known as the Coriolis force or effect (click here to see an animation)), the whole storm starts to spiral around a central more calm point, known as the eye. The pressures and weather are more stable in the eye, as the updrafts of air are balanced by descending cooled air.
As tropical storms pass over land they lose their source of energy, and the die out. You can see an animated guide to this process at the BBC.