Numerical integration of a steady state vorticity equation for barotropic currents (defined as the deepwater currents) provides estimates of the residual circulation over a continential shelf region that are consistent with a given dynamic height field. The threshold in time scale for motions for which these estimates apply is given by the inverse of the product of the Coriolis parameter f and the ratio of the thickness Δ&tgr; of a topographic boundary layer to the longshore scale and is typically 20 days. In this steady limit, within a Δ&tgr; distance (~50 km) from the coast, a flow of frictional equilibrium prevails in which turbulent vertical transfer of momentum enters as surface and bottom stresses. The stress at the shelf bottom proves to be easily expressible as proportional to the barotropic current velocity with a proportionality fΔ cosα, where Δ stands for the displacement thickness and α for the total angle of veering through the bottom Ekman layer. An application to the Coastal Upwelling Experiment 1 data off Oregon demonstrates the skill of the computation in that for a proper choice of Δ it accounts for over 75% of the observed longshore difference in both the longshore and onshore-offshore velocity components at the 60-m depth between two pairs of current meter moorings along the 100-m isobath