A two-dimensional modeling study by Moffat and Lentz recently reported that downwelling-favorable wind can induce cross-shore upwelling circulation within a bottom-attached, buoyant coastal current. Here, we extend the problem to three dimensions. The driving mechanism and the sensitivity for the upwelling circulation are studied, using a primitive equation ocean model and an analytical model. After the initial downwelling adjustment that steepens the isopycnals and compresses the coastal current, the cross-shore flow can switch to steady upwelling circulation. This reverse circulation coincides with a vertically well-mixed water column and persists until interrupted by the arrival of river plume bulge from upstream. During the upwelling phase, the ageostrophic cross-shore flow follows the Ekman balance. The sense of cross-shore circulation is governed by a dimensionless parameter, the shear ratio, which measures the relative size of geostrophic shear and velocity shear supported by the wind in the shallow-water limit. Upwelling circulation occurs when the shear ratio is greater than one. This condition represents that, near the surface, the wind-intensified pressure gradient exceeds the maximum possible Coriolis force associated with the wind-forced, alongshore flow. The resulting upwelling circulation acts to slump the isopycnals to restore the geostrophic balance. Therefore, within a coastal current, decreasing wind stress in fact strengthens the upwelling circulation, as a weaker wind produces a weaker shear and thus increases the imbalance. This inverse relation holds until the wind is too weak to mix the water column. Based on the analytical model, a regime classification for the cross-shore circulation under downwelling-favorable wind is proposed. An observational example is given.
