This paper presents a one-dimensional model of katabatic winds in ambient flow and examines types of possible solutions. Results presented in dimensionless form indicate that 1) cooling along a slope with upslope ambient flow can lead to tranquil (flow speed less than gravity wave speed) solutions characterized by appreciable entrainment, and 2) the onset time of katabatic winds is particularly sensitive to the retarding effects of opposing flow and reduced cooling rates. Model results present a plausible explanation for observed delays in the onset time of downslope flow of up to 8 h after sunset along certain humid tropical slopes.