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Kial D. Stewart, Graham O. Hughes, and Ross W. Griffiths

Abstract

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 ¼ 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.

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Graham O. Hughes, Andrew Mc C. Hogg, and Ross W. Griffiths

Abstract

The overturning circulation of the global oceans is examined from an energetics viewpoint. A general framework for stratified turbulence is used for this purpose; first, it highlights the importance of available potential energy in facilitating the transfer of kinetic energy to the background potential energy (defined as the adiabatically rearranged state with no motion). Next, it is shown that it is the rate of transfer between different energy reservoirs that is important for the maintenance of the ocean overturning, rather than the total amount of potential or kinetic energy. A series of numerical experiments is used to assess which energy transfers are significant in the overturning circulation. In the steady state, the rate of irreversible diapycnal mixing is necessarily balanced by the production of available potential energy sourced from surface buoyancy fluxes. Thus, the external inputs of available potential energy from surface buoyancy forcing and of kinetic energy from other sources (such as surface winds and tides, and leading to turbulent mixing) are both necessary to maintain the overturning circulation.

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Juan A. Saenz, Rémi Tailleux, Edward D. Butler, Graham O. Hughes, and Kevin I. C. Oliver

Abstract

The study of the mechanical energy budget of the oceans using the Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically rearranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which is illustrated using climatological data, the authors show that compressibility effects are in fact minor. The reference state can be regarded as a well-defined one-dimensional function of depth, which forms a surface in temperature, salinity, and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. This study shows that the reference state obtained by standard sorting methods is equivalent to, though computationally more expensive than, the volume frequency distribution approach. The approach that is presented can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

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Catherine A. Vreugdenhil, Andrew McC. Hogg, Ross W. Griffiths, and Graham O. Hughes

Abstract

The relative roles of advective processes and mixing on the temporal adjustment of the meridional overturning circulation are examined, in particular the effects of mixing in either the abyssal or upper ocean. Laboratory experiments with convectively driven overturning and imposed stirring rates show that the circulation adjusts toward an equilibrium state on time scales governed by mixing in the upper boundary layer region but independent of the mixing rate in the bulk of the interior. The equilibrium state of the stratification is dependent only on the rate of mixing in the boundary layer. An idealized high-resolution ocean model shows adjustment (of a two-cell circulation) dominated primarily by the advective ventilation time scale, consistent with a view of the circulation determined by water mass transformation occurring primarily near the surface. Both the experiments and the model results indicate that adjustments of the circulation are controlled by surface buoyancy uptake (or rejection) and that the nonequilibrium circulation is dominated by advective processes, especially if the average abyssal ocean diffusivity is less than 3 × 10−5 m2 s−1.

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