This article is from the Storms FAQ, by Chris Landsea firstname.lastname@example.org with numerous contributions by others.
Surprisingly, not much lightning occurs in the inner core (within
about 100 km or 60 mi) of the tropical cyclone center. Only around a
dozen or less cloud-to-ground strikes per hour occur around the eyewall
of the storm, in strong contrast to an overland mid-latitude mesoscale
convective complex which may be observed to have lightning flash rates
of greater than 1000 per hour (!) maintained for several hours.
Hurricane Andrew's eyewall had less than 10 strikes per hour from the
time it was over the Bahamas until after it made landfall along Louisiana,
with several hours with no cloud-to-ground lightning at all (Molinari et
al. 1994). However, lightning can be more common in the outer cores of
the storms (beyond around 100 km or 60 mi) with flash rates on the order
of 100s per hour.
This lack of inner core lightning is due to the relative weak nature
of the eyewall thunderstorms. Because of the lack of surface heating
over the ocean ocean and the "warm core" nature of the tropical cyclones,
there is less buoyancy available to support the updrafts. Weaker updrafts
lack the super-cooled water (e.g. water with a temperature less than 0 C
or 32 F) that is crucial in charging up a thunderstorm by the interaction
of ice crystals in the presence of liquid water (Black and Hallett 1986).
The more common outer core lightning occurs in conjunction with the
presence of convectively-active rainbands (Samsury and Orville 1994).
One of the exciting possibilities that recent lightning studies
have suggested is that changes in the inner core strikes - though the
number of strikes is usually quite low - may provide a useful forecast
tool for intensification of tropical cyclones. Black (1975) suggested
that bursts of inner core convection which are accompanied by increases
in electrical activity may indicate that the tropical cyclone will soon
commence a deepening in intensity. Analyses of Hurricanes Diana (1984),
Florence (1988) and Andrew (1992), as well as an unnamed tropical storm
in 1987 indicate that this is often true (Lyons and Keen 1994 and Molinari
et al. 1994).