Determining the cross-shelf and vertical scales of coastal upwelling

Idealized primitive equation numerical model experiments are used to investigate the source waters (as defined by a passive tracer of initial depth) for coastal upwelling over a uniformly sloping bottom and allowing for alongshore variability in the wind stress. Under steady conditions, the volume of upwelled water is essentially balanced by alongshore transport from the direction (“downwave”) toward which long coastal-trapped waves propagate. For weak stratification (s = αN/f ≪ 0.1 where α is the bottom slope, N the initial buoyancy frequency and f the Coriolis parameter) this alongshore transport involves a balance of bottom Ekman pumping and topographic vortex stretching: the “arrested topographic wave”. For larger s, some of this alongshore transport occurs in a frontal jet. When time dependence is included, a third offshore scale, determined by frontal motion balancing local Ekman transport, enters initially, while the frontal equilibrium scale dominates after longer times. The offshore scale translates readily into a maximum depth from which upwelled waters can reach the surface. Scalings are provided for the source water depth in both the steady and unsteady cases. Broadly speaking, the source depth is greater when alongshore winds or bottom slope are stronger, or when the alongshore extent of wind forcing is greater. Some variants, including the effects of a more realistic shelf-slope topography, are also examined.