Gravity waves (GWs) with horizontal wavelengths of 32-2000 km are investigated during tropical cyclone (TC) Ivan (2008) in the southwest Indian Ocean in the upper troposphere (UT) and the lower stratosphere (LS) using observational data sets, radiosonde and GPS radio occultation data, ECMWF analyses and simulations of the French numerical model Meso-NH with vertical resolution < 150 m near the surface and 500 m in the UT/LS. Observations reveal dominant low-frequency GWs with short vertical wavelengths of 0.7-3 km, horizontal wavelengths of 80-400 km and periods of 4.6-13 h in the UT/LS. Continuous wavelet transform and image-processing tools highlight a wide spectrum of GWs with horizontal wavelengths of 40-1800 km, short vertical wavelengths of 0.6-3.3 km and periods of 20 min-2 days from modelling analyses. Both ECMWF and Meso-NH analyses are consistent with radiosonde and GPS radio occultation data, showing evidence of a dominant TC-related quasi-inertia GW propagating eastward east of TC Ivan with horizontal and vertical wavelengths of 400-800 km and 2-3 km respectively in the LS, more intense during TC intensification. In addition, the Meso-NH model produces a realistic, detailed description of TC dynamics, some high-frequency GWs near the TC eye, variability of the tropospheric and stratospheric background wind and TC rainband characteristics at different stages of TC Ivan. A wave number 1 vortex Rossby wave is suggested as a source of dominant inertia GW with horizontal wavelengths of 400-800 km, while shorter scale modes (100-200 km) located at northeast and southeast of the TC could be attributed to strong localized convection in spiral bands resulting from wave number 2 vortex Rossby waves. Meso-NH simulations also reveal GW-related clouds east of TC Ivan.