# Info

Fig. 4.70 Thermal structure of the equatorial thermocline (vertical axis depicts depth in m): contour labels are temperature (in °C), overlaid with the vertical gradient (in °C/100 m).

insightful studies, Pedlosky (1987b, 1996) developed a theory for the dynamical connection between the subtropical thermocline and the Equatorial Undercurrent, and our discussion below is based on his theory. The essence of the theory is that, to the lowest order, the Equatorial Undercurrent can be treated in terms of the ideal-fluid model. In order to conserve potential vorticity, the inertial term is retained near the equator.

First, there is a small latitudinal band near the equator where geostrophy breaks down. To replace geostrophy, we search for a new balance between the inertial terms and other terms. The outer edge of this special zone can be defined as the latitude where the Coriolis term is equal to the inertial term. The commonly used Rossby number is defined as

Near the equator, the Coriolis parameter is approximately f = Py (4.399)

Approaching the equator, f declines; therefore the Rossby number Ro = U/Py2 increases. Thus, within a distance of df, df =4U]p (4.400)

the advection term, or the relative vorticity, will be dynamically important. From observations, U & 1 m/s, P = 2.28 x 10-11/s/m; thus, df & 208 km. Accordingly, within 2 degrees off the equator, we expect that the inertial terms in the momentum equation will be non-negligible.

In this section we study the equatorial thermocline and current in the framework of inertial current, i.e., our study will focus on the dynamical effect of inertial terms and the linkage of the Equatorial Undercurrent, as an inertial current, with currents in the off-equatorial regimes. Study in this section will be complemented by the study of communication between the subtropics and tropics in the next section. Since the Equatorial Undercurrent is linked to the ventilated thermocline at mid latitudes, we will first describe the ventilated thermocline in the extra-equatorial regime.

### 4.6.2 The extra-equatorial solution

The equatorial thermocline is studied as an extension from the framework of the ventilated thermocline by Luyten et al. (1983). The ocean is simulated in terms of a 2j-layer model formulated on an equatorial j-plane (Fig. 4.71). As shown in Figure 4.70, the main thermocline outcrops in the eastern part of the Pacific and Atlantic Oceans, so we set the layer thickness to zero along the eastern boundary.

The solution off equator is described by the ventilated thermocline model discussed in Section 4.1.7.