The flow of turbidity currents and pyroclastic flows into regions with topography produces spatial variation in flow. This variation (the flow nonuniformity) affects not only the loci of deposition but also the depositional facies. The nonuniformity around topography can be characterized by a dimensionless parameter, the internal Froude number, F i , that is dependent upon flow velocity, the reciprocal of flow height, and the density stratification. Low values of F i result in decoupling of the flow into a lower, denser part that moves around the topography and an upper part that moves up or over it. We present an example from an Oligocene turbidite system interacting with a bounding slope. Massive sands on the open basin floor pass laterally into thinner sands with abundant traction structures adjacent to the paleoslope. We use outcrop constraints to develop a simple model of the basinal paleotopography, and the nonuniformity of flows resulting from their interactions with it. The observed facies variation with respect to the paleotopography corresponds closely with predictions based on this pattern of nonuniformity. Currents were deflected by the slope, but there is also evidence of reflection where the lower-density parts of the flows ran up the slope and collapsed back onto the basin floor. Application of an internal Froude number criterion indicates that the flows had a very steep density gradient, at least in their lower parts, that resulted in deflection of the basal parts of the flows. This model may be generally applicable for predicting facies variation in turbidites and pyroclastic deposits where topography has been an important control during deposition.