Why Is the Deep Sinking Narrow?

Abstract

Narrowness of downwelling and broadness of upwelling are ubiquitous features of numerical and laboratory simulations of oceanic thermal overturning and are evidenced by the global ocean distributions of tracers, heat, and salt. By varying the relative size of the upwelling and downwelling in a pipe model based upon that of Stommel, it is shown that this structure has two interesting energetic properties: 1) broad upwelling allows the maximum amount of overturning for a given forcing by allowing the deepest penetration of heat and hence the largest baroclinic pressure gradient and 2) the narrow sinking region solution has the minimum potential energy because the deep is filled with the coldest possible water formed beneath the coldest boundary condition. The spinup of a two-dimensional model from diffusive equilibrium (with an initial symmetric overturning) to advective-diffusive-convective steady state shows that the asymmetry develops as baroclinic pressure gradients weaken preferentially on the upwelling side of the overturning while the flow of fluid modified by the boundary condition away from the surface tends to maintain pressure gradients in the downwelling branch. In steady-state solutions, the asymmetry develops as the relative importance of advection is increased by decreasing the diffusivity.