A two-dimensional (in a vertical and meridional plane) model for steady equatorial undercurrents is described. Compared to the primitive equation model, the zonal pressure gradient and associated zonal temperature gradients (both vary vertically) are prescribed in this model, and all other terms involving zonal variations are ignored. With zonal pressure gradients resembling actual ocean gradients, model undercurrents agree well with observations as far as the main features are concerned. In particular, the model simulates a stronger undercurrent in the Pacific than in the Atlantic, suggesting that a weaker zonal wind stress, a shallower thermocline, a more surface-confined zonal pressure gradient, and an associated larger magnitude of near-surface zonal temperature gradient around 30°W in the Atlantic than around 150°W in the Pacific, which is related to the longitudinal structure of the zonal wind stress and longitudinal basin extent, are the cause of this difference. An argument based on geostrophy and heat balance is also given.
The model is used to examine the dynamic nature and heat balance of steady equatorial undercurrents for a symmetric circulation about the equator. With a full, nonlinear heat balance, an undercurrent is generated in both linear and nonlinear dynamic balances, but the dynamical features are different in the two cases. In the nonlinear dynamic case, vertical-momentum transports play a key role; in the linear dynamic case, though the eastward zonal pressure gradient provides a necessary forcing, the existence of the undercurrent also relies on the meridional diffusive momentum transport near the surface, which is positive instead of negative. For a doubling of zonal wind stress and a fixed vertical profile of zonal pressure gradient, the speed of the undercurrent core increases by about 25% in the nonlinear case but remains unchanged in the linear case; surface temperature increases by about 1.3 K in the nonlinear case and decreases by 3 K in the linear case.
Within the undercurrent core, the dominant momentum balance is between the zonal pressure gradient and meridional diffusive friction, and the heat balance is between zonal and vertical advections. It is proposed that the position of the undercurrent core relative to the thermocline reflects different advective heat balances: the undercurrent core is above (or below) the thermocline if the net heat advection balance tends to heat (or cool). The fact that the undercurrent core is more or less in the thermocline suggests that three-dimensional advective heat transports almost cancel each other.