The turbulent impinging jet flows associated with vertical or short take-off and landing (VTOL) aircraft hovering in ground effect can have a critical effect on aircraft performance, and they are modeled very poorly by existing models. Three flow phenomena representative of VTOL ground effects flows, the upwash fountain, the ground vortex, and the impingement zone of a round jet, are considered. Extensions to the k-ϵ model are presented which are designed to account for streamline curvature, large scale mixing, and anisotropy. The extensions significantly improve the model's ability to predict some aspects of these flows. Requirements for further model development are identified.