144
Vertical Structure: Baroclinic Quasi-Geostrophic Models
upper and lower layer across the pool boundary. This shows up in the figure as
a kink in the upper layer streamlines at the pool boundary and is especially
evident in the figure towards the southwest terminus of the pool boundary.
In the parameter setting of Fig. 3.9.2, where H1 = H2 and y 1 = y 2 , it
follows from (3.9.11) and (3.9.12) that the meridional velocity in the upper
layer in the pool is exactly twice as large as the meridional velocity in the lower
layer. If the density difference between the two layers, Y~> should diminish, the
meridional flow would become increasingly barotropic. The zonal flow has a
vertical shear:
(3.9.14)
large enough to tilt the interface and offset the planetary potential vorticity
gradient even as the ratio yJ!y 2 ____, 0.
The criterion (3.9.9) has another interpretation more closely related to a
possible mechanism for setting the lower layers into motion. In the absence of
motion in layer 2 (and all lower layers) the potential vorticity in layer 2 would
be given by:
q2 = [Jy + F2t/11
= [Jy + Ft/Js·
(3.9.15)
Along the northern boundary of the gyre the flow is strictly zonal, and the
potential vorticity gradient is in the meridional direction. On y = L the
gradient of potential vorticity in layer 2 is given by:
8q2 = [3 +F8t/ls
8y
8y
=[3-Fus.
(3.9.16)
Therefore the condition that the Rossby wave be arrested by the
barotropic zonal flow is equivalent to the condition that the meridional
potential vorticity gradient vanishes at the point x, on the northern boundary.
Further westward, where us is larger, the potential vorticity gradient in layer 2
is negative, while it is positive in the upper layer, as the reader may verify. Thus
along the northern boundary of the pool the conditions for baroclinic
instability are satisfied (Pedlosky 1987). The instability produces eddies on
scales of the order of the deformation radius, i.e., quite small compared to the
gyre scale, so that the application of the theory for the instability of
horizontally uniform flows can be applied to the slowly varying (on the eddy
scale) gyre scale flow. One of the principal effects of baroclinically produced
eddies is vertically to transfer the momentum of the mean flow so as to reduce
the vertical shear which is the source of the instability. This sets layer 2 into
motion. Thus the emergence of the closed geostrophic contours, isolating a
Vertical Structure: Baroclinic Quasi-Geostrophic Models
upper and lower layer across the pool boundary. This shows up in the figure as
a kink in the upper layer streamlines at the pool boundary and is especially
evident in the figure towards the southwest terminus of the pool boundary.
In the parameter setting of Fig. 3.9.2, where H1 = H2 and y 1 = y 2 , it
follows from (3.9.11) and (3.9.12) that the meridional velocity in the upper
layer in the pool is exactly twice as large as the meridional velocity in the lower
layer. If the density difference between the two layers, Y~> should diminish, the
meridional flow would become increasingly barotropic. The zonal flow has a
vertical shear:
(3.9.14)
large enough to tilt the interface and offset the planetary potential vorticity
gradient even as the ratio yJ!y 2 ____, 0.
The criterion (3.9.9) has another interpretation more closely related to a
possible mechanism for setting the lower layers into motion. In the absence of
motion in layer 2 (and all lower layers) the potential vorticity in layer 2 would
be given by:
q2 = [Jy + F2t/11
= [Jy + Ft/Js·
(3.9.15)
Along the northern boundary of the gyre the flow is strictly zonal, and the
potential vorticity gradient is in the meridional direction. On y = L the
gradient of potential vorticity in layer 2 is given by:
8q2 = [3 +F8t/ls
8y
8y
=[3-Fus.
(3.9.16)
Therefore the condition that the Rossby wave be arrested by the
barotropic zonal flow is equivalent to the condition that the meridional
potential vorticity gradient vanishes at the point x, on the northern boundary.
Further westward, where us is larger, the potential vorticity gradient in layer 2
is negative, while it is positive in the upper layer, as the reader may verify. Thus
along the northern boundary of the pool the conditions for baroclinic
instability are satisfied (Pedlosky 1987). The instability produces eddies on
scales of the order of the deformation radius, i.e., quite small compared to the
gyre scale, so that the application of the theory for the instability of
horizontally uniform flows can be applied to the slowly varying (on the eddy
scale) gyre scale flow. One of the principal effects of baroclinically produced
eddies is vertically to transfer the momentum of the mean flow so as to reduce
the vertical shear which is the source of the instability. This sets layer 2 into
motion. Thus the emergence of the closed geostrophic contours, isolating a