The time and spatial evolution of gravity-wave characteristics are analysed using wavelets in vertical profiles of temperature and winds at Tromelin Island (15.53¿S, 54.31¿E) during the passage of the intense tropical cyclone Hudah in the Southern Ocean Indian Basin in 2000. Inertia-gravity waves were observed in the upper troposphere and the lower stratosphere with dominant vertical wavelengths of 1.5--3 km, horizontal wavelengths <2000 km and periods of 0.6--1.6 days. Large amounts of gravity-wave energy were detected during landfalls of the tropical cyclone. The distribution of total energy indicates that mesoscale convective structures such as tropical cyclones are important gravity-wave sources in the upper troposphere.