Observations and Modelling of Fronts and Frontogenesis

111.1 Introduction
In this chapter we combine a simple representation of a
stratified interior with a previously-developed theory for
strong horizontal gradients in a surface mixed layer (de
Szoeke and Richman, 1984) to develop a model for the wind-
driven upwelling of a stratified fluid. We apply the model
to the case of coastal upwelling. The interior consists of
two homogeneous layers of differing density. The mixed layer
resolves the fronts that form as layer interfaces "surface"
at the coast and are advected offshore. Combining these
elements allows the modelling of the upwelling and
entrainment into the surface layer of deep, dense interior
fluid that is initially separated from the surface layer by
an intermediate layer of less-dense fluid.
We employ two principal analytical simplifications: we
specify that all flow variables be uniform in the alongshore
direction, and that semigeostrophic dynamics apply.
These semigeostrophic equations are similar to those
developed by Hoskins and Bretherton (1972) for the study of
atmospheric frontogenesis (subsequently generalized to three
dimensions by Hoskins (1975)). They were used by Pedlosky
(1978) in an adiabatic model of the onset of upwelling driven
by a mass sink at the coast and an alongshore pressure
gradient.
47