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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 numberSas 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 highS, 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 StatementWind-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.
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A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope
Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS2forS< 1 and is in better agreement with numerical simulations.
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- Award ID(s):
- 1947954
- PAR ID:
- 10467793
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 53
- Issue:
- 10
- ISSN:
- 0022-3670
- Format(s):
- Medium: X Size: p. 2317-2330
- Size(s):
- p. 2317-2330
- Sponsoring Org:
- National Science Foundation
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