Towards a theory for the Indo-Pacific middepth stratification

The Pacific Ocean appears exponentially stratified between 1 and 3 km depth with a decay scale on the order of 1 km. In his celebrated paper Abyssal Recipes, Walter Munk proposed a theoretical explanation of these observations by suggesting a pointwise buoyancy balance between the upwelling of cold water with the downward diffusion of heat. Assuming a constant upwelling velocity w and turbulent diffusivity κ, the model yields an exponential stratification whose decay scale is consistent with observations if κ ~ 10-4 m2 s-1. Over time, much effort has been made to reconcile Munk's ideas with evidence of vertical variability in κ, but comparably little emphasis has been placed on the even stronger evidence that w decays towards the surface. In particular, w nearly vanishes at 1 km depth. In light of these observations we consider a variable-coefficient, basin-averaged analogue of Munk's budget, which we verify against a hierarchy of numerical models ranging from an idealized basin-and-channel configuration to a coarse global ocean simulation. Study of the budget reveals that the observed decay of w requires a concurrent decay in κ to produce an exponential-like stratification. As such, the frequently cited value of 10-4 m2 s-1 is representative only of the bottom of the mid-depths, whereas κ must be much smaller above. The decay of mixing in the vertical is as important to the stratification as its magnitude.