Effect of Entrainment
359
6.6 Effect of Entrainment
Observations of the EUC (e.g., Lukas 1986; see also the review by Wacongne
1989) show that in the Pacific, for example, the EUC weakens considerably
from the central ocean towards the eastern boundary. This is consistent with
the study of Bryden and Brady (1985) who showed the simultaneous rise of the
undercurrent core with longitude and the entrainment of fluid from the EUC
into the upper surface layer. This entrainment is limited to the upper portion of
the current, but as the current shallows this transfer of fluid into the upper
layer becomes an increasingly significant fraction of the transport. As each
upward sloping density layer reaches the mixed layer, it is peeled off the top of
the current and enters the mixed layer, and flows away from the equator driven
by the wind as Ekman transport . Layer after layer is thus stripped off the top
of the undercurrent, finally producing the observed cold pool of water on the
surface in the eastern equatorial oceans as the deeper layers rise to the surface.
Pedlosky (1988), following the diagnosis of Bryden and Brady, argued that this
entrainment is the principal mechanism for the termination of the undercurrent. This is suggested by a simple consideration of the mass balance in the
EUC which quantifies the description just given.
Consider the meridional Ekman transport directed away from the equator
at a distance £ from the equator, i.e., from the flanks of the EUC. This
transport, over the basin width Lx, is of the order:
ro
TEkman = Pof3£Lx
(6.6.1)
where r0 is the scale of the westward directed wind stress. The eastward mass
flux in the undercurrent, on the other hand, is of the order:
YzH
roLx
TEuC = UHf= f3£Z H£ = Pof3£ = TEkman
(6.6.2)
if the scaling relations (6.3.21) are used.
This implies that the transport of the EUC can be completely exhausted by
the off-equator mass flux driven by the Ekman transport which is fed, as
described by Bryden and Brady (1985), by the entrainment of undercurrent
fluid from the upper portion of the EUC. Although the introduction of a
shadow zone halts the acceleration of the current by eliminating the east-west
pressure gradient, a dissipative mechanism is required to explain its termination. The cross-isopycnal mass flux represents such a nonadiabatic effect, and
its inclusion in the dynamics of the undercurrent, as does its effect on the
interior discussed in Chapter 5, requires a fundamental alteration of the physics
of the model.
Pedlosky (1988) introduced a simple, heuristic model for the effect of the
entrainment due to cross-isopycnal mixing which requires only minor alterations in the calculations although introducing fundamental changes in the
359
6.6 Effect of Entrainment
Observations of the EUC (e.g., Lukas 1986; see also the review by Wacongne
1989) show that in the Pacific, for example, the EUC weakens considerably
from the central ocean towards the eastern boundary. This is consistent with
the study of Bryden and Brady (1985) who showed the simultaneous rise of the
undercurrent core with longitude and the entrainment of fluid from the EUC
into the upper surface layer. This entrainment is limited to the upper portion of
the current, but as the current shallows this transfer of fluid into the upper
layer becomes an increasingly significant fraction of the transport. As each
upward sloping density layer reaches the mixed layer, it is peeled off the top of
the current and enters the mixed layer, and flows away from the equator driven
by the wind as Ekman transport . Layer after layer is thus stripped off the top
of the undercurrent, finally producing the observed cold pool of water on the
surface in the eastern equatorial oceans as the deeper layers rise to the surface.
Pedlosky (1988), following the diagnosis of Bryden and Brady, argued that this
entrainment is the principal mechanism for the termination of the undercurrent. This is suggested by a simple consideration of the mass balance in the
EUC which quantifies the description just given.
Consider the meridional Ekman transport directed away from the equator
at a distance £ from the equator, i.e., from the flanks of the EUC. This
transport, over the basin width Lx, is of the order:
ro
TEkman = Pof3£Lx
(6.6.1)
where r0 is the scale of the westward directed wind stress. The eastward mass
flux in the undercurrent, on the other hand, is of the order:
YzH
roLx
TEuC = UHf= f3£Z H£ = Pof3£ = TEkman
(6.6.2)
if the scaling relations (6.3.21) are used.
This implies that the transport of the EUC can be completely exhausted by
the off-equator mass flux driven by the Ekman transport which is fed, as
described by Bryden and Brady (1985), by the entrainment of undercurrent
fluid from the upper portion of the EUC. Although the introduction of a
shadow zone halts the acceleration of the current by eliminating the east-west
pressure gradient, a dissipative mechanism is required to explain its termination. The cross-isopycnal mass flux represents such a nonadiabatic effect, and
its inclusion in the dynamics of the undercurrent, as does its effect on the
interior discussed in Chapter 5, requires a fundamental alteration of the physics
of the model.
Pedlosky (1988) introduced a simple, heuristic model for the effect of the
entrainment due to cross-isopycnal mixing which requires only minor alterations in the calculations although introducing fundamental changes in the