Under fair weather conditions the time-averaged, wind-driven current forms a spiral in which the current vector decays and turns clockwise with increasing depth. These spirals resemble classical Ekman spirals. They differ in that their rotation depth scale exceeds the e-folding depth of the speed by a factor of 2 to 4 and they are compressed in the downwind direction. A related property is that the time-averaged stress is evidently not parallel to the time-averaged vertical shear. We develop the hypothesis that the flat spiral structure may be a consequence of the temporal variability of stratification. Within the upper 10--20 m of the water column this variability is associated primarily with the diurnal cycle and can be treated by a time-dependent diffusion model or a mixed-layer model. The latter can be simplified to yield a closed solution that gives an explicit account of stratified spirals and reasonable hindcasts of midlatitude cases. At middle and higher latitudes the wind-driven transport is found to be trapped mainly within the upper part of the Ekman layer, the diurnal warm layer. At tropical latitudes the effects of diurnal cycling are in some ways less important, and Ekman layer currents are likely to be significant to much greater depths. In that event the lower part of the Ekman layer is likely to be affected by stratification variability that may be nonlocal. ¿ 1999 American Geophysical Union