Parameter Study of a Continuously Stratified Model of the Ideal-Fluid Thermocline*
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The parameter sensitivity of a continuously stratified model of the ideal-fluid thermocline in the subtropical gyre interior is studied. A one-dimensional advection-diffusion model is used to set up a background stratification that can provide both the potential vorticity function for the unventilated thermocline and the mixed layer depth used in the ideal-fluid thermocline model. The wind-driven circulation is treated as a perturbation to this background stratification. Although the perturbation solution excludes mixing/diffusion, the dynamic effect of diapycnal mixing is included in the unperturbed solution; therefore, the ideal-fluid solution should correspond to a nonzero diffusion solution for the wind-driven and thermohaline circulation in the ocean. It is shown that the model can reproduce the thermocline structure, which corresponds to either finite or infinitely weak mixing. Under the extreme weak diffusion limit, the model produces a thermocline that looks like a step function in the stratification, which separates the wind-driven gyre above it and the stagnant abyssal water underneath it. It is shown that the subduction rate and production of mode water with low-potential vorticity are closely related to the stratification (or the potential vorticity) of the unventilated thermocline, the geometry of the mixed layer, the Ekman pumping rate, and the orientation of the intergyre boundary. Changes in the structure of the thermocline in response to different upper boundary conditions are explored. It is found that cooling and southward migration of the jet stream induce the production of low potential vorticity mode water, while changes in the vertical density profile have an appearance like the second baroclinic mode.