The Importance of Nonlinear Cross-Shelf Momentum Flux during Wind-Driven Coastal Upwelling*

A simple theory is proposed for steady, two-dimensional, wind-driven coastal upwelling that relates the dynamics and the structure of the cross-shelf circulation to the stratification, bathymetry, and wind stress. The new element is an estimate of the nonlinear cross-shelf momentum flux divergence due to the wind-driven cross-shelf circulation acting on the vertically sheared geostrophic alongshelf flow. The theory predicts that the magnitude of the cross-shelf momentum flux divergence relative to the wind stress depends on the Burger number S = αN/f, where α is the bottom slope, N is the buoyancy frequency, and f is the Coriolis parameter. For S ≪ 1 (weak stratification), the cross-shelf momentum flux divergence is small, the bottom stress balances the wind stress, and the onshore return flow is primarily in the bottom boundary layer. For S ≈ 1 or larger (strong stratification), the cross-shelf momentum flux divergence balances the wind stress, the bottom stress is small, and the onshore return flow is in the interior. Estimates of the cross-shelf momentum flux divergence using moored observations from four coastal upwelling regions (0.2 ≤ S ≤ 1.5) are substantial relative to the wind stress when S ≈ 1 and exhibit a dependence on S that is consistent with the theory. Two-dimensional numerical model results indicate that the cross-shelf momentum flux divergence can be substantial for the time-dependent response and that the onshore return flow shifts from the bottom boundary layer for small S to just below the surface boundary layer for S ≈ 1.5–2.