A two-dimensional numerical model is used to simulate nocturnal drainage flow in a small urban valley with light prevailing winds and conditions of supercritical Richardson numbers (Ri). The model uses a hydrostatic and Boussinesq system of equations written in terrain-following coordinates. Radiative transfer is represented by Brunt's method of radiative diffusivity. Eddy diffusivities are specified in the subgrid parameterization for conditions where Ri is supercritical. Tests show the dependence of drainage wind on slope angle, cooling rate, surface drag and prevailing wind speed, and also the insensitivity of wind and temperature to the eddy diffusivities under supercritical Ri conditions. The drainage wind cells are asymmetric, with a shallow surface layer of drainage flow and a thicker upper region of slower return flow. The predicted wind profiles show low-level maxima and the predicted temperature profiles are exponential in shape, in good agreement with observations obtained in Edmonton, Alberta in the summer of 1978. The model is also able to predict the quasi-stationary slope flow observed in the field.