The Role of Turbulent Mixing in an Overturning Circulation Maintained by Surface Buoyancy Forcing

The role of externally imposed rates of small-scale mixing in an overturning circulation forced by differential surface buoyancy fluxes is examined in a laboratory experiment. The circulation occupies the full volume and involves a dense turbulent plume against the endwall and a broad upwelling throughout the interior. For strong externally imposed stirring, turbulent diffusion is the primary means of vertical density transport in the flow, and the dependence of the equilibrated circulation on the mixing rate accords with a theoretical model; the overturning rate increases as the 1/4 power of the turbulent diffusivity. For weak externally imposed stirring, advection is the dominant mechanism of vertical density transport, and the circulation is independent of the rate of external stirring. The rate of vertical density transport is parameterized as a bulk diffusivity obtained from different methods, including one from a Munk-like advection-diffusion balance and another from the transport of buoyancy across the surface. For strong stirring, the bulk diffusivities returned by the various methods agree with the externally imposed mixing rate. However, the parameterizations implicitly include a nondiffusive component of vertical transport associated with advection of the density field and it is shown that, for weak stirring, the bulk diffusivities exceed the externally imposed mixing rate. For the oceans, results suggest that the primary effect of mixing (with energy sourced from winds, tides, and convection) is to deepen the thermocline, thereby influencing the entrainment and consequent vertical transport of density in the dense sinking regions. It is concluded that this advective transport of density, and not vertical mixing, is crucial for coupling the surface to the abyss.