118
Vertical Structure: Baroclinic Quasi-Geostrophic Models
must travel along the paths traced out by these curves. The geostrophic
contours are shaped by the flow itself. In the quasi-geostrophic approximation
the curves are completely determined once the Sverdrup transport is calculated.
Thus the shape of the contours depends directly on the structure of the wind
forcing and its strength. When the wind forcing is weak, the shape of the
geostrophic contours is determined by the p term, and the geostrophic contours
coincide with latitude circles. As the strength of the wind forcing increases, the
contours can become increasingly distorted from latitude circles. This effect is
also favored by large values ofF, i.e., either by a weak stratification or by small
layer thicknesses. The basic physics of this distortion of the geostrophic
contours lies in the variation of the interface between layers 1 and 2 forced by
the wind-driven circulation. To obtain an intuitive understanding of the
shaping of the contours, note that if layer 2 were at rest q2 would be equal to
q2• In this case the full Sverdrup transport would be carried in the upper layer.
In order for layer 2 to be at rest the interface between layer 1 and layer 2 must
slope to eliminate any pressure gradient in the second layer according to
(3.2.13a). The thickness of layer 2 therefore varies even if the layer is at rest.
This alters the field of the potential vorticity in the second layer and distorts the
geostrophic contours. Note that the gesotrophic contours obtained in this
thought experiment in which layer 2 is at rest are the same contours that would
obtain if layer 2 is in motion. In this more general case q2 differs from q2
although their isolines coincide by (3.5.14).
The geostrophic contours are also the characteristic curves of the linear
partial differential equation (3.5.10). Information is propagated along the
characteristic curves. In particular the information concerning the eastern
boundary condition of no normal flow is carried along the geostrophic
contours to points within the basin.
Since the Sverdrup streamfunction (3.5.8) always vanishes at the eastern
boundary, the geostrophic contours near the eastern boundary of the ocean
become identical with latitude circles. Hence a geostrophic contour emanates
from each point on the eastern boundary and initially trends westward along a
latitude circle (see Fig. 3.5.1). If the wind forcing is strong enough, the curves
become increasingly distorted and the possibility arises that the curves become
bent around certain regions. If the forcing is strong enough, the bending can
become so great that the geostrophic contours close on themselves, as shown in
the figure, isolating the enclosed regions from the eastern boundary. Into those
regions girdled by a geostrophic contour, information about the eastern
boundary is unable to penetrate.
Since t/1 2 is constant along the geostrophic contours, the lower layer
streamfunction must be zero on all the geostrophic contours that strike the
eastern boundary where t/1 2 is zero. Hence along all contours such as the one
labeled A in Fig. 3.5.1 there can be no motion in the nondissipative limit. The
flow is blocked on all such contours and in such regions the entire Sverdrup
transport is carried in the upper layer. In the island regions or pools, such as the
area marked Pin the figure, the contours do not strike the eastern boundary,
Vertical Structure: Baroclinic Quasi-Geostrophic Models
must travel along the paths traced out by these curves. The geostrophic
contours are shaped by the flow itself. In the quasi-geostrophic approximation
the curves are completely determined once the Sverdrup transport is calculated.
Thus the shape of the contours depends directly on the structure of the wind
forcing and its strength. When the wind forcing is weak, the shape of the
geostrophic contours is determined by the p term, and the geostrophic contours
coincide with latitude circles. As the strength of the wind forcing increases, the
contours can become increasingly distorted from latitude circles. This effect is
also favored by large values ofF, i.e., either by a weak stratification or by small
layer thicknesses. The basic physics of this distortion of the geostrophic
contours lies in the variation of the interface between layers 1 and 2 forced by
the wind-driven circulation. To obtain an intuitive understanding of the
shaping of the contours, note that if layer 2 were at rest q2 would be equal to
q2• In this case the full Sverdrup transport would be carried in the upper layer.
In order for layer 2 to be at rest the interface between layer 1 and layer 2 must
slope to eliminate any pressure gradient in the second layer according to
(3.2.13a). The thickness of layer 2 therefore varies even if the layer is at rest.
This alters the field of the potential vorticity in the second layer and distorts the
geostrophic contours. Note that the gesotrophic contours obtained in this
thought experiment in which layer 2 is at rest are the same contours that would
obtain if layer 2 is in motion. In this more general case q2 differs from q2
although their isolines coincide by (3.5.14).
The geostrophic contours are also the characteristic curves of the linear
partial differential equation (3.5.10). Information is propagated along the
characteristic curves. In particular the information concerning the eastern
boundary condition of no normal flow is carried along the geostrophic
contours to points within the basin.
Since the Sverdrup streamfunction (3.5.8) always vanishes at the eastern
boundary, the geostrophic contours near the eastern boundary of the ocean
become identical with latitude circles. Hence a geostrophic contour emanates
from each point on the eastern boundary and initially trends westward along a
latitude circle (see Fig. 3.5.1). If the wind forcing is strong enough, the curves
become increasingly distorted and the possibility arises that the curves become
bent around certain regions. If the forcing is strong enough, the bending can
become so great that the geostrophic contours close on themselves, as shown in
the figure, isolating the enclosed regions from the eastern boundary. Into those
regions girdled by a geostrophic contour, information about the eastern
boundary is unable to penetrate.
Since t/1 2 is constant along the geostrophic contours, the lower layer
streamfunction must be zero on all the geostrophic contours that strike the
eastern boundary where t/1 2 is zero. Hence along all contours such as the one
labeled A in Fig. 3.5.1 there can be no motion in the nondissipative limit. The
flow is blocked on all such contours and in such regions the entire Sverdrup
transport is carried in the upper layer. In the island regions or pools, such as the
area marked Pin the figure, the contours do not strike the eastern boundary,