Abstract Spectral analyses of time series of zonal winds derived from locations of balloons drifting in the Southern Hemisphere polar vortex during the Vorcore campaign of the Stratéole program reveal a peak with a frequency near 0.10 h−1, more than 25% higher than the inertial frequency at locations along the trajectories. Using balloon data and values of relative vorticity evaluated from the Modern Era Retrospective-Analyses for Research and Applications (MERRA), the authors find that the spectral peak near 0.10 h−1 can be interpreted as being due to inertial waves propagating inside the Antarctic polar vortex. In support of this claim, the authors examine the way in which the low-frequency part of the gravity wave spectrum sampled by the balloons is shifted because of effects of the background flow vorticity. Locally, the background flow can be expressed as the sum of solid-body rotation and shear. This study demonstrates that while pure solid-body rotation gives an effective inertial frequency equal to the absolute vorticity, the latter gives an effective inertial frequency that varies, depending on the direction of wave propagation, between limits defined by the absolute vorticity plus or minus half of the background relative vorticity.