216
Theory of the Ventilated Thermocline
Aside from the increased complexity of the solution and its higher
resolution the basic structure of the solution is qualitatively similar to that
already described by the simpler two-layer model.
4.8 The Subpolar Gyre
We saw in Chapter 3 that within quasi-geostrophic theory there is no essential
difference in the dynamics of the subpolar and subtropical gyres. If WE changes
sign from negative to positive, the quasi-geostrophic equations admit a
solution for the subpolar gyre which is identical to the subtropical gyre under a
reflection around the latitude of zero Ekman pumping and a change of sign of
the streamfunction. With the planetary scale equations, which allow an order
one variation in the interface depths, the situation is quite different. The
mathematical symmetry no longer exists, and this reflects a fundamental
distinction in the physics of the two gyres.
It is not at all clear whether the adiabatic model that we are using is
appropriate for the subpolar gyre, or even whether the Sverdrup balance, in
which the interaction with the bottom is ignored, is valid there. A diagnostic
study by Luyten et al. (1985) suggests the importance of cross-isopycnal fluxes
and of bottom topography and therefore casts doubt on both of the
assumptions of the present model. In Chapter 5 we discuss the circulation of
the subpolar gyre under the influence of nonadiabatic cooling by crossisopycnal fluxes. However, it suffices for now to demonstrate the distinctive
dynamical character of the subpolar gyre by extending the adiabatic ventilated
thermocline solution northward across the zero Ekman pumping line.
In the region just north of the latitude of zero Ekman pumping, at e = 00 ,
where f = fo, only layer 3 in our three-layer model is directly acted upon by
the Ekman vertical velocity, which in the subpolar gyre is an upward suction
into the mixed layer of the fluid beneath. Suppose we assume, as we did for the
subtropical gyre, that in the region near e = 00 only layer 3 is in motion. Then
(4.7.1) is valid in this region as well:
(4.8.1)
where now however, do, given by (4.7.2), is negative because WE is positive in
the subpolar gyre. As we progress away from the line of zero Ekman pumping
D5 tends to get larger in magnitude, i.e., more negative. The interface, z4,
between layers 3 and 4, is pulled upwards, and layer 3 becomes increasingly
thinner. If the Ekman suction is strong enough, the interface surfaces, and
layer 3 vanishes along the line <1>3(0), given by:
(4.8.2)
Theory of the Ventilated Thermocline
Aside from the increased complexity of the solution and its higher
resolution the basic structure of the solution is qualitatively similar to that
already described by the simpler two-layer model.
4.8 The Subpolar Gyre
We saw in Chapter 3 that within quasi-geostrophic theory there is no essential
difference in the dynamics of the subpolar and subtropical gyres. If WE changes
sign from negative to positive, the quasi-geostrophic equations admit a
solution for the subpolar gyre which is identical to the subtropical gyre under a
reflection around the latitude of zero Ekman pumping and a change of sign of
the streamfunction. With the planetary scale equations, which allow an order
one variation in the interface depths, the situation is quite different. The
mathematical symmetry no longer exists, and this reflects a fundamental
distinction in the physics of the two gyres.
It is not at all clear whether the adiabatic model that we are using is
appropriate for the subpolar gyre, or even whether the Sverdrup balance, in
which the interaction with the bottom is ignored, is valid there. A diagnostic
study by Luyten et al. (1985) suggests the importance of cross-isopycnal fluxes
and of bottom topography and therefore casts doubt on both of the
assumptions of the present model. In Chapter 5 we discuss the circulation of
the subpolar gyre under the influence of nonadiabatic cooling by crossisopycnal fluxes. However, it suffices for now to demonstrate the distinctive
dynamical character of the subpolar gyre by extending the adiabatic ventilated
thermocline solution northward across the zero Ekman pumping line.
In the region just north of the latitude of zero Ekman pumping, at e = 00 ,
where f = fo, only layer 3 in our three-layer model is directly acted upon by
the Ekman vertical velocity, which in the subpolar gyre is an upward suction
into the mixed layer of the fluid beneath. Suppose we assume, as we did for the
subtropical gyre, that in the region near e = 00 only layer 3 is in motion. Then
(4.7.1) is valid in this region as well:
(4.8.1)
where now however, do, given by (4.7.2), is negative because WE is positive in
the subpolar gyre. As we progress away from the line of zero Ekman pumping
D5 tends to get larger in magnitude, i.e., more negative. The interface, z4,
between layers 3 and 4, is pulled upwards, and layer 3 becomes increasingly
thinner. If the Ekman suction is strong enough, the interface surfaces, and
layer 3 vanishes along the line <1>3(0), given by:
(4.8.2)