Photo above from: NASA. Storm track below from here. Megi is a Korean word for catfish.
Moisture rising off the warm ocean waters in the tropics causes a mass of cloud buildup (unless there are strong winds aloft). As the water vapor rises, incoming air flows in toward the rising column of moisture. The incoming air is deflected to the right, and the Coriolis force starts the whole mass spinning, somewhat counterintuitively, counterclockwise in the northern hemisphere. An excellent simple graphic can be found here. The clouds aloft become larger and more organized, at some point reaching 39-73 mph, at which time the storm is designated as a "tropical storm". In satellite views, an indication of the tropical storm stage is the appearance of the spiral arms that spin off from the main mass. Because the air is spinning, the rotation keeps the moist air from collapsing into the very center, the so-called "eye" of the hurricane. The winds spiral around the eye, up the wall of the eye (the "eye wall"), and down the eye itself. Thunder and lightning can be intense in the spiraling arms outside the eye wall.
Typhoons in the Pacific (or hurricanes in the Atlantic) are storms that originate in the tropics. Two conditions there favor the creation of large storms: warm water (27C or warmer) and the strong Coriolis effect near the equator (10-30 latitude). The main condition that prevents development of typhoons is strong winds in the troposphere. In the northern hemisphere, the Coriolis force causes anything moving in the northern hemisphere to be deflected to the right (to the left in the southern hemisphere).
In the Pacific, the typhoons originate in Micronesia, and regularly hit the Philippines as is the case with Typhoon Megi. In the Atlantic, most hurricanes originate off the west coast of Africa and then veer northward toward the Caribbean, the Gulf of Mexico, southern U.S., the east coast, and ultimately, eastern Canada. An excellent simple graphic of the formation conditions for typhoons or hurricanes can be found here.
If sustained winds reach 74 mph, the storm is officially designated as a hurricane or typhoon. They are typically about 300 miles across, and travel at 15-60 mph until they encounter land, where they rapidly dissipate into "mere" strong rain storms. When Megi made landfall in the Philippines, it was more than 370 miles across. It was the most intense tropical cyclone of 2010 to date.
On the Saffir-Simpson Hurricane scale, Typhoon Megi is a catagory 5, with damage predicted to be "catastrophic". Central pressure in the eye can be <920 mb (compared to >980 mb for smaller category 1 storms, wind speeds >155 mph, and storm surges >18 feet. Hurricane Mitch in October, 1998 left over 9,200 people dead in Honduras, destroyed over 150,000 homes, and caused ~$1 billion in crop damage. Peak sustained winds in Megi have been reported at 180 mph, with gusts estimated to 220 mph. For those interested in aeronautics, these peak winds are Mach number 0.3!!
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