Wind-induced constraints on the mass and buoyancy transports in a simple adiabatic model of the ocean circulation

The issue of how much diapycnal mixing occurs in the ocean remains a hotly debated question whose answer is needed to understand the nature of the oceanic component of the meridional heat transport in the climate system. From a theoretical viewpoint, this issue is intimately linked to the issue of what controls the large-scale density structure of the ocean, the so-called thermocline problem. In this regard, the ideas have evolved from the linear advective-diffusive view originally proposed by Robinson and Stommel (1959) to the purely advective view of the ideal fluid thermocline theory proposed at the same time by Welander (1959). This shift was largely due to the success of the ventilated thermocline theory of Luyten, Pedlosky, and Stommel (1983), and to mounting observational evidence suggesting values of diapycnal mixing lower by an order of magnitude than previously thought. Although an adiabatic view of the ocean circulation seems contradictory with the need for diapycnal mixing obviously required to support meridional heat transport, the contradiction is only apparent because adiabatic models only apply to the ocean interior, i.e., away from the surface and boundary layers. This realization has recently led several authors to develop ocean models allowing diapycnal mixing only within localized lateral and internal boundary layers. So far, this idea has been illustrated in several numerical studies, with some success, but theoretical analytical models are still to be developed. As a first step toward an analytical theory for the mass and buoyancy transports in the ocean, we show how to determine analytically the mass and buoyancy transports implicit in the popular ventilated thermocline model but previously left unaddressed. We show that such a model successfully represents the upper wind-driven cells of the ocean circulation, as well as the meridional heat transport in the subtropical gyre. However, because this type of model assumes a deep resting ocean, it does not possess any deep meridional overturning cells, and thus has a meridional heat transport with the wrong sign at mid-latitudes. Nevertheless, these results are encouraging enough to suggest that the ventilated thermocline model, originally intended to describe the wind-driven circulation in a subtropical gyre, can in fact be used as the first building stone of a theory for the meridional overturning circulation and its associated mass and heat transports.