An analysis is made to determine the properties and scales for the setup of upwelling driven by an impulsively started, steady, uniform wind of semi-infinite fetch. The backward edge of the wind field acts as a geographical origin for the generation of coastal-trapped waves (CTWs). A perturbation analysis is used to show that prior to the arrival of the nth mode CTW, the alongshore velocity is shown to asymptote to a constant value, (set by bottom drag) and over a timescale Tn. As this viscous limit is achieved, the upwelling becomes increasingly confined to the bottom boundary layer and bottom stress balances wind stress: Interior upwelling is shut down. The viscous limit may not be achieved, since after the arrival of the nth CTW mode, a gradient in the alongshore velocity is set up and its divergence acts to feed the offshore Ekman transport and shut the upwelling down. Numerical results are used to show that the frictional length and timescales predicted by the perturbation analysis are unrealistically small due to an underestimation of thermal wind shear. Moreover, the theory underpredicts the importance of the first CTW mode, which is shown to largely determine the setup and shutdown of upwelling. A simple first-mode model for upwelling is developed and used to evaluate the validity of a numerical, open boundary condition in determining the correct degree of upwelling. A case study for the Chilean shelf is presented.