434
[31 vdz = fwo
abyss
Abyssal Circulation
(7.7.2)
assuming that the bottom of the abyss is fiat or that the vertical velocity is
negligibly small there. If w0 = 0 in the western region which the anomaly has
reached by Rossby wave propagation, then locally the integral of the
meridional velocity must vanish although v itself, from (7. 7.1 ), differs from
zero. That is, the barotropic portion of the abyssal flow can be locally negligible
compared to the baroclinic part if the upwelling velocity varies strongly in the
horizontal. The flow must therefore be layered, at least in the western region of
the basin. If a thermal anomaly is produced on the eastern boundary of the
basin, say, by the Kelvin wave propagated from the source region or from a
region of upwelling further south rather than by local upwelling, the flow is
layered even in the eastern basin if the upwelling is weak there as well. Thus the
layering of the abyssal flow can be associated with the spatial non uniformity of
the abyssal upwelling.
Pedlosky (1992) and Edwards and Pedlosky (1995) studied a continuously
stratified, linear model of the abyssal circulation to examine this phenomenon.
In particular, the model is used to examine the relation between the structure of
the abyssal flow in both the interior and the boundary layer and the vertical
structure of the sources on the perimeter of the basin representing the sources
of deep water in the abyss. As might be expected from the indirect nature of the
forcing of the interior, the relationship between the vertical structure of the
input sources and the vertical structure of the interior flow is a complex one.
The model dynamics consists of geostrophic balance for the velocities
outside the region of the western boundary current as well as the hydrostatic
approximation. The total density field, as in the quasi-geostrophic models of
Chapter 3, is represented in terms of a background field which is independent
of horizontal position plus a weak anomaly which varies laterally, namely:
Ptotal =Po+ Pv(z) + PH(x, y,z).
(7.7.3)
The basic restriction of the model is that
PH « Pv «Po·
(7.7.4)
Thus the density is nearly constant and has a weak vertical variation which
determines a background buoyancy frequency:
N = -gapv
(
)
1/2
Po az
(7.7.5)
and an even weaker lateral variation of density that drives a baroclinic motion
through the thermal wind relation. Thus, again using Cartesian coordinates for
simplicity:
p 0 fv = apjax
[31 vdz = fwo
abyss
Abyssal Circulation
(7.7.2)
assuming that the bottom of the abyss is fiat or that the vertical velocity is
negligibly small there. If w0 = 0 in the western region which the anomaly has
reached by Rossby wave propagation, then locally the integral of the
meridional velocity must vanish although v itself, from (7. 7.1 ), differs from
zero. That is, the barotropic portion of the abyssal flow can be locally negligible
compared to the baroclinic part if the upwelling velocity varies strongly in the
horizontal. The flow must therefore be layered, at least in the western region of
the basin. If a thermal anomaly is produced on the eastern boundary of the
basin, say, by the Kelvin wave propagated from the source region or from a
region of upwelling further south rather than by local upwelling, the flow is
layered even in the eastern basin if the upwelling is weak there as well. Thus the
layering of the abyssal flow can be associated with the spatial non uniformity of
the abyssal upwelling.
Pedlosky (1992) and Edwards and Pedlosky (1995) studied a continuously
stratified, linear model of the abyssal circulation to examine this phenomenon.
In particular, the model is used to examine the relation between the structure of
the abyssal flow in both the interior and the boundary layer and the vertical
structure of the sources on the perimeter of the basin representing the sources
of deep water in the abyss. As might be expected from the indirect nature of the
forcing of the interior, the relationship between the vertical structure of the
input sources and the vertical structure of the interior flow is a complex one.
The model dynamics consists of geostrophic balance for the velocities
outside the region of the western boundary current as well as the hydrostatic
approximation. The total density field, as in the quasi-geostrophic models of
Chapter 3, is represented in terms of a background field which is independent
of horizontal position plus a weak anomaly which varies laterally, namely:
Ptotal =Po+ Pv(z) + PH(x, y,z).
(7.7.3)
The basic restriction of the model is that
PH « Pv «Po·
(7.7.4)
Thus the density is nearly constant and has a weak vertical variation which
determines a background buoyancy frequency:
N = -gapv
(
)
1/2
Po az
(7.7.5)
and an even weaker lateral variation of density that drives a baroclinic motion
through the thermal wind relation. Thus, again using Cartesian coordinates for
simplicity:
p 0 fv = apjax