Observations and Modelling of Fronts and Frontogenesis

interior layers, on the horizontal scale of the local
internal deformation radius.
The uppermost interior layer eventually becomes
entrained completely into the surface layer in the upwelling
region, leaving only two layers there. We derive matching
conditions to join the two-layer region with the three-layer
region. Sustained upwelling results in a step-like
horizontal profile of surface layer density, as the interior
layer interface "surfaces" and is advected offshore as a
front in the surface layer. The upwelled horizontal density
profile scales with an internal deformation radius calculated
from the initial fields.
III.2.a Equations
111.2 Model formulation
Figure 111.1 displays the model geometry. We use a
right-handed Cartesian coordinate system with origin at the
surface on the coastal boundary, x alongshore, y positive
offshore, and z vertical. We specify that all flow variables
be uniform in the alongshore direction and take the flow to
be governed by the semigeostrophic equations (e.g. , Pedlosky,
1979, Sec. 8.4): the geostrophic balance holds normal to
shore, while the alongshore acceleration is retained at
lowest order. The main effect of imposing semigeostrophy is
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