Stream Function Representation of Velocity Fields in a Terrain Following Coordinate System The stream function representation of the velocity field for an infinitely long uniform ridge is developed through the solution of Poisson's partial differential equation. This problem is transformed into an associated problem by means fo terrain-following coordinates because the lower boundary condition is difficult to impose in the original coordinate system. The associated domain is then discretized and solutions are approximated by finite difference methods. Results for potential flow are then compared to known analytic solutions as a means to evaluate the performance of the code. The code is then further adapted to the specialize task of producing the streamlines which correspond to the velocity field produced by a complex mesoscale atmospheric numerical model which also uses terrain-following coordinates and has been stripped of all imposed physical constraints which are inconsistent with potential flow. These solutions are then compared and contrasted with previously obtained potential flow results.