Time-Dependent Linear Theory for the Generation of Poleward Undercurrents on Eastern Boundaries

Abstract

AbstractA time-dependent, inviscid, linear theory for the generation of poleward undercurrent flow under upwelling conditions along midlatitude ocean eastern boundaries is proposed. The theory relies on a conceptual separation of time scales between the rapid, coastal-trapped wave response to upwelling winds and the subsequent slow, interior, quasigeostrophic evolution. Solutions are obtained under idealized conditions in which the coastal boundary and the continental-slope topography are uniform alongshore, and the time-dependent wind-stress forcing is applied over a limited meridional range, uniform cross-shore, and directed alongshore. A time-dependent coastal boundary condition on the slow-time-scale interior flow, consisting of the low-frequency, geostrophically balanced sea surface height disturbance over the outer shelf, is obtained from consideration of the fast-time-scale, coastal-trapped response. A quasigeostrophic potential vorticity equation is then solved to determine the interior response to this time-dependent boundary condition. Under upwelling conditions, the results show the formation of a localized region of subsurface poleward flow over the upper continental slope that is qualitatively consistent in amplitude, location, and timing with observations of poleward undercurrents on eastern boundaries. Despite its origin as a sea surface height anomaly, the coastal-boundary condition drives a baroclinic planetary wave response, in which the poleward subsurface flow evolves in planetary vorticity balance with induced subsurface upwelling.