Abstract. Atmospheric gravity waves play a key role in the transfer of energy and momentum between layers of the Earth's atmosphere. However, nearly all general circulation models (GCMs) seriously under-represent the momentum fluxes of gravity waves at latitudes near 60∘ S, which can lead to significant biases. A prominent example of this is the “cold pole problem”, where modelled winter stratospheres are unrealistically cold. There is thus a need for large-scale measurements of gravity wave fluxes near 60∘ S, and indeed globally, to test and constrain GCMs. Such measurements are notoriously difficult, because they require 3-D observations of wave properties if the fluxes are to be estimated without using significant limiting assumptions. Here we use 3-D satellite measurements of stratospheric gravity waves from NASA's Atmospheric Infrared Sounder (AIRS) Aqua instrument. We present the first extended application of a 3-D Stockwell transform (3DST) method to determine localised gravity wave amplitudes, wavelengths and directions of propagation around the entire region of the Southern Ocean near 60∘ S during austral winter 2010. We first validate our method using a synthetic wavefield and two case studies of real gravity waves over the southern Andes and the island of South Georgia. A new technique to overcome wave amplitude attenuation problems in previous methods is also presented. We then characterise large-scale gravity wave occurrence frequencies, directional momentum fluxes and short-timescale intermittency over the entire Southern Ocean. Our results show that highest wave occurrence frequencies, amplitudes and momentum fluxes are observed in the stratosphere over the mountains of the southern Andes and Antarctic Peninsula. However, we find that around 60 %–80 % of total zonal-mean momentum flux is located over the open Southern Ocean during June–August, where a large “belt” of increased wave occurrence frequencies, amplitudes and fluxes is observed. Our results also suggest significant short-timescale variability of fluxes from both orographic and non-orographic sources in the region. A particularly striking result is a widespread convergence of gravity wave momentum fluxes towards latitudes around 60∘ S from the north and south. We propose that this convergence, which is observed at nearly all longitudes during winter, could account for a significant part of the under-represented flux in GCMs at these latitudes.