Representation of convective plumes by vertical adjustment

Open-ocean deep-water formation involves the interplay of two dynamical processes; plumes (less than or equal to 1 km wide), driven by ''upright'' convection, and geostrophic eddies (greater than or equal to 5 km wide), driven by baroclinic instability. Numerical ''twin'' experiments are used to address two questions about the plumes: Can they be represented by a simple mixing process in large-scale models? If so, is it important that the mixing occurs over a finite time t(mix), or would instantaneous mixing produce the same effect on large-scale properties? In numerical simulations which resolve the geostrophic eddies, we represent the plumes with a ''slow'' convective adjustment algorithm which is broadly equivalent to an enhanced vertical diffusivity of density in statically unstable regions. The diffusivity kappa depends on t(mix), the mixing timescale. The fidelity of the plume parameterization is then evaluated by comparison with plume-resolving simulations of open-ocean deep convection. Integral properties of the plumes, such as the temperature census of the convected water and the strength of the rim current that encircles the convecting region, are all accurately reproduced by the slow adjustment scheme. The importance of choosing an appropriate finite value for t(mix) is explored by setting t(mix) = 12 hours in some experiments, in accordance with scaling considerations, and t(mix) = 0 in others, corresponding to instantaneous adjustment, the conventional assumption. In the case of convection into a moderately or strongly stratified ocean the behavior does not significantly depend on t(mix). However, in neutral conditions the slow adjustment does improve the parametric representation. Our experiments confirm the picture of plumes homogenizing the water column over a time t(mix).