3 Vertical Structure:
Baroclinic Quasi-Geostrophic Models
3.1 Introduction
Observations of the general circulation of the oceans, described briefly in
Chapter 1, show that the most vigorous motion, driven primarily by the wind,
takes place in the upper 1-2 km of the ocean and then diminishes dramatically
with depth. Although it is difficult to obtain reliable measurements of timeaveraged velocity in the midocean because of the presence of fluctuations on
time scales of months, the signature of this intensification of the velocity field
near the upper boundary of the ocean is evident in the more easily observed
density field of the oceans. The thermal wind relation (see below) relates the
vertical shear of the horizontal velocity to the horizontal density gradient.
Therefore regions of sharp density variations horizontally can be identified as
regions of strong currents. Figure 3.1.1, taken from the Levitus Atlas (1982),
shows a zonal average of the density field in the Atlantic Ocean. The region of
strong density gradient is seen to be limited to the upper ocean. The horizontal
and vertical density gradients are captured largely in tbe upper 1 km and
diminish sharply with depth. This phenomenon of the rapid drop-off with
depth of the motion and the associated variations of the density field presents
us with a theoretical problem which is fundamental to our understanding of the
dynamics of the ocean, while being at the same time of considerable difficulty.
The link between the density field and the velocity means that the problem of
explaining the observed oceanic density field is nothing less than the problem of
explaining the full three-dimensional structure of the oceanic circulation.
In Chapter 2 we saw that the theory of even the homogeneous model of the
ocean circulation still presents theoretical challenges and difficulties that have
not been completely overcome. The homogeneous model tells us nothing about
the vertical structure of the ocean's circulation, and we would therefore expect
a theory for the baroclinic circulation to be even more complex. Nevertheless,
noteworthy progress has been made on the problem of the vertical structure of
the ocean circulation in recent years. In most cases the discussion has
concentrated on theories for the structure of the flow in the midocean, at
distances removed from the regions of strong western boundary currents. In all
cases a starting point of the theoretical development has been acceptance of the
Sverdrup balance for the vertical average of the circulation in the interior. We
Baroclinic Quasi-Geostrophic Models
3.1 Introduction
Observations of the general circulation of the oceans, described briefly in
Chapter 1, show that the most vigorous motion, driven primarily by the wind,
takes place in the upper 1-2 km of the ocean and then diminishes dramatically
with depth. Although it is difficult to obtain reliable measurements of timeaveraged velocity in the midocean because of the presence of fluctuations on
time scales of months, the signature of this intensification of the velocity field
near the upper boundary of the ocean is evident in the more easily observed
density field of the oceans. The thermal wind relation (see below) relates the
vertical shear of the horizontal velocity to the horizontal density gradient.
Therefore regions of sharp density variations horizontally can be identified as
regions of strong currents. Figure 3.1.1, taken from the Levitus Atlas (1982),
shows a zonal average of the density field in the Atlantic Ocean. The region of
strong density gradient is seen to be limited to the upper ocean. The horizontal
and vertical density gradients are captured largely in tbe upper 1 km and
diminish sharply with depth. This phenomenon of the rapid drop-off with
depth of the motion and the associated variations of the density field presents
us with a theoretical problem which is fundamental to our understanding of the
dynamics of the ocean, while being at the same time of considerable difficulty.
The link between the density field and the velocity means that the problem of
explaining the observed oceanic density field is nothing less than the problem of
explaining the full three-dimensional structure of the oceanic circulation.
In Chapter 2 we saw that the theory of even the homogeneous model of the
ocean circulation still presents theoretical challenges and difficulties that have
not been completely overcome. The homogeneous model tells us nothing about
the vertical structure of the ocean's circulation, and we would therefore expect
a theory for the baroclinic circulation to be even more complex. Nevertheless,
noteworthy progress has been made on the problem of the vertical structure of
the ocean circulation in recent years. In most cases the discussion has
concentrated on theories for the structure of the flow in the midocean, at
distances removed from the regions of strong western boundary currents. In all
cases a starting point of the theoretical development has been acceptance of the
Sverdrup balance for the vertical average of the circulation in the interior. We