Chris Landsea, Science and Operations Officer at NOAA’s National Hurricane Center, writes:
During each hurricane season, there always appear suggestions that one should simply use nuclear weapons to try and destroy the storms.
Apart from the fact that this might not even alter the storm, this approach neglects the problem that the released radioactive fallout would fairly quickly move with the tradewinds to affect land areas and cause devastating environmental problems.
Needless to say, this is not a good idea.
[...]
The main difficulty with using explosives to modify hurricanes is the amount of energy required.
A fully developed hurricane can release heat energy at a rate of 5 to 20x1013 watts and converts less than 10% of the heat into the mechanical energy of the wind.
The heat release is equivalent to a 10-megaton nuclear bomb exploding every 20 minutes.
According to the 1993 World Almanac, the entire human race used energy at a rate of 1013 watts in 1990, a rate less than 20% of the power of a hurricane.
In addition, an explosive, even a nuclear explosive, produces a shock wave, or pulse of high pressure, that propagates away from the site of the explosion somewhat faster than the speed of sound. Such an event doesn't raise the barometric pressure after the shock has passed because barometric pressure in the atmosphere reflects the weight of the air above the ground.