Nonlinear Dynamics over the Inner Shelf and in the Surface Boundary Layer during Coastal Upwelling

Abstract Theoretical understanding of the upward vertical motion into the surface layer during coastal upwelling is often based on steady linear Ekman dynamics. In steady linear theory, the divergence of surface transport that leads to upwelling is associated with either overlap of the frictional boundary layers over the inner shelf or wind stress curl farther offshore. However, the alongshore current associated with a coastal upwelling front is associated with relative vorticity which modifies surface transport. A new nonlinear theory shows that, under spatially uniform wind forcing, the fraction of Ekman transport upwelled over the inner shelf tends to decrease with increasing slope Burger number S as the baroclinic alongshore jet strengthens and cyclonic vorticity increases. Similar patterns are shown in a set of idealized numerical experiments. Unsteadiness in the alongshore flow, neglected in the theory, strongly influences the cross-shelf distribution of upwelling in the numerical model at locations offshore of the inner shelf and near the core of the upwelling jet. The theory and numerical modeling are extended to explore the effect of a large-scale alongshore pressure gradient force (PGF) that forms in response to alongshore variations in wind stress. At high S , a baroclinic PGF is associated with a shallow onshore return flow, but the fraction of modeled upwelling that occurs over the inner shelf is not strongly affected. The results emphasize that the strength and location of the alongshore jet strongly influence the cross-shelf distribution of coastal upwelling in the presence of stratification and a sloping bottom. Significance Statement Wind-driven coastal upwelling is important for supplying nutrients to phytoplankton at the base of marine ecosystems. This study uses simple models to investigate factors that determine where upwelling of water into the surface layer occurs when wind blows along the coastline. With a larger difference in density between the surface and bottom layers, a steeply sloping seafloor, and at latitudes closer to the equator, the upwelling region shifts farther offshore because of the strength and location of faster ocean currents that flow along the coastline.