Abstract A common bias in global circulation models (GCMs) is an overly strong and thus too cold Southern Hemisphere (SH) wintertime stratospheric polar vortex with important implications for simulating the ozone hole. Additionally, the jet axis in GCMs is too straight in the vertical compared to reanalyses. Both biases have posed a long‐standing challenge to GCMs. Here, we use a development version of the Community Atmosphere Model (CAM) with different horizontal resolutions. The high‐resolution simulations exhibit a smaller bias in the representation of the SH polar vortex. Motivated by these results we introduce a gravity wave source parameterization to represent frontal gravity waves that have been missing in CAM. In this parameterization fronts are represented by their vorticity. Both, the amplitude and the phase speed of the launched waves are dependent on characteristics of the frontal systems. Introducing this parameterization led to significant improved SH stratospheric polar vortex in CAM.