Recent research into river channel con¯uences has identi®ed con¯uence geometry, and particularly bed discordance, as a control on con¯uence ¯ow structures and mixing processes, and this has been illustrated using both ®eld measurements in natural con¯uences and laboratory measurements of simpli®ed con¯uences. Generalization of the results obtained from these experiments is limited by the number of con¯uence geometries that can be examined in a reasonable amount of time. This limitation may be overcome by numerical models, in which con¯uence geometry is more readily varied, and data acquired more rapidly. This paper aims to: (i) validate the application of a three-dimensional numerical model to a simple con¯uence geometry; (ii) simulate the eects of dierent boundary condition values upon ¯ow structures; and (iii) interpret the implications of these simulations for river channel con¯uence dynamics. The model used in this research solves the three-dimensional form of the Navier±Stokes equations and is used to simulate the ¯ow in a parallel con¯uence of unequal depth channels and to investigate the eect of dierent combinations of velocity and depth ratio between the two tributaries. The results generally agree with empirical evidence that secondary circulation is generated in the absence of streamline curvature, but only for speci®c combinations of depth and velocity ratio. This research shows how understanding of the interaction of these controls is enhanced if pressure gradients are considered. The velocity ratio is the prime determinant of the cross-stream pressure gradient that initiates cross-stream velocities. However, for signi®cant secondary circulation to form, crossstream velocities must lead to signi®cant transfer of ¯uid in the cross-stream direction. This depends on the vertical extent of the cross-stream pressure gradient which is controlled by the depth ratio. In this study, strong secondary circulation occurred for a depth dierential of 25% or more, as long as the velocity in the shallower tributary was at least as great as that in the deeper channel. This provides an important context for interpretation of previous work and for the design of new experiments in both the ®eld and the laboratory.