An investigation is made of the two-dimensional flow of a stratified fluid over an extended obstacle, characterized by a source disturbance, for an infinite medium and for a layer of finite depth. The problems are posed as initial-boundary value problems, and steady-state solutions for the flow field are obtained in the limit of large time. The results show an unattenuated system of jets or shear layers extending far upstream from the obstacle, which occurs whenever a system of lee waves is present. For the finite depth case detailed calculations are made, starting with realistic mean values for the atmosphere. The final established profile indicates a variable shear and density profile far upstream, characterized by variable local Richardson numbers. The wind shears induced are also of the order of shears due to thermal wind effects, though quite apart from these effects. The study therefore points to the importance of topographical features on vertical wind shear in the troposphere.