AbstractRecent observational and numerical studies have investigated the dynamics of fine‐scale gravity waves radiating horizontally outward from tropical cyclones. The waves are wrapped into spirals by the tangential wind of the cyclone and are described as spiral gravity waves. This study addresses how well numerical simulations of these waves compare to observations as the horizontal grid spacing is decreased from 2.0 to 1.0 to 0.5 km, and the number of vertical levels changes from 25 to 50 to 100. Spectral filtering is applied to separate the fine‐scale waves in vertical velocity (w) and the larger‐scale waves in pressure (p) from moist updrafts and downdrafts in the eyewall and rainbands. As the grid spacing decreases, the radial wavelengths of the w waves decrease from 20 to 7 km, approaching observed values. For grid spacing 1.0 km, the p waves become well‐resolved with wavelength 70 km. The outward phase speeds range from 15 to 30 ms−1 for the w waves and 50 to 70 ms−1 for p waves. Analysis of the upper‐level outflow region finds that the spiral w waves propagate 5–10 ms−1 faster due to radial advection, but also finds what appear to be different classes of larger‐amplitude, slow‐moving spiral waves. Similar waves can be seen in satellite images, which appear to be caused by dynamical instability of the strongly vertically sheared radial and tangential winds in the TC outflow.