On frontal and ventilated models of the main thermocline

A new similarity approach is applied to the thermocline equations in order to examine contrasting frontal and ventilated models of the main thermocline. The method of solution involves reducing the number of independent variables of the controlling partial differential equation, leading to a particular form for the solutions which satisfy appropriate boundary conditions. A frontal model of the thermocline is obtained following the study of Salmon and Hollerbach (1991). When the vertical diffusivity becomes vanishingly small, an interior front in the subtropical gyre appears at the depth where the vertical velocity changes sign. The front separates downwelling warm water in the subtropical gyre from the underlying upwelling of cold, deep water. These solutions appear to be robust to changes in the vertical diffusivity profile, as long as there is a small, nonzero value in the interior. However, when there is uniform diffusivity, there is no implied surface heat flux and surface isotherms are coincident with streamlines. As the diffusivity increases toward the surface, the surface heat input increases in magnitude and the temperature field becomes more plausible. A ventilated model of the thermocline is formed using the similarity approach with a diffusive surface boundary-layer overlying an adiabatic interior. In this case, the temperature and velocity fields are solved for in the limit of uniform potential vorticity. There is now a more plausible cross-isothermal flow in the surface layer with a polewards decrease in temperature, and the implied surface heat input increases equatorwards. Fluid is subducted from the surface boundary layer into the adiabatic interior and forms a continuous thermocline. In conclusion, the contrasting frontal and ventilated solutions arise from modeling different aspects of the circulation, rather than depending on the type of model employed. The ventilated solutions form a thermocline by advecting the surface temperature field into the interior of a subtropical gyre, whereas the frontal solutions create a thermocline from the interaction of the wind-driven gyre and the underlying thermohaline circulation. These thermocline solutions might occur separately or together in the real ocean, although both solutions might be modified by higher-order processes or more complicated forcing