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Juan A. Saenz, Qingshan Chen, and Todd Ringler

Abstract

Recent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWA framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, the analysis is verified by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.

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Henk A. Dijkstra, Juan A. Saenz, and Andrew McC. Hogg

Abstract

Oscillatory behavior of the Atlantic meridional overturning circulation (MOC) is thought to underlie Atlantic multidecadal climate variability. While the energy sources and sinks driving the mean MOC have received intense scrutiny over the last decade, the governing energetics of the modes of variability of the MOC have not been addressed to the same degree. This paper examines the energy conversion processes associated with this variability in an idealized North Atlantic Ocean model. In this model, the multidecadal variability arises through an instability associated with a so-called thermal Rossby mode, which involves westward propagation of temperature anomalies. Applying the available potential energy (APE) framework from stratified turbulence to the idealized ocean model simulations, the authors study the multidecadal variability from an energetics viewpoint. The analysis explains how the propagation of the temperature anomalies leads to changes in APE, which are subsequently converted into the kinetic energy changes associated with variations in the MOC. Thus, changes in the rate of generation of APE by surface buoyancy forcing provide the kinetic energy to sustain the multidecadal mode of variability.

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Andrew McC. Hogg, Henk A. Dijkstra, and Juan A. Saenz

Abstract

A well-studied example of natural climate variability is the impact of large freshwater input to the polar oceans, simulating glacial melt release or an amplification of the hydrological cycle. Such forcing can reduce, or entirely eliminate, the formation of deep water in the polar latitudes and thereby weaken the Atlantic meridional overturning circulation (MOC). This study uses a series of idealized, eddy-permitting numerical simulations to analyze the energetic constraints on the Atlantic Ocean's response to anomalous freshwater forcing. In this model, the changes in MOC are not correlated with the global input of mechanical energy: both kinetic energy and available potential energy (APE) increase with northern freshwater forcing, while the MOC decreases. However, a regional analysis of APE density supports the notion that local maxima in APE density control the response of the MOC to freshwater forcing perturbations. A coupling between APE input and changes in local density anomalies accounts for the difference in time scales between the recovery and collapse of the MOC.

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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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Todd Ringler, Juan A. Saenz, Phillip J. Wolfram, and Luke Van Roekel

Abstract

The exact, three-dimensional, thickness-weighted averaged (TWA) Boussinesq equations are used to diagnose eddy–mean flow interaction in an idealized circumpolar current (ICC). The force exerted by mesoscale eddies on the TWA velocity is expressed as the divergence of the Eliassen–Palm flux tensor. Consistent with previous findings, the analysis indicates that the dynamically relevant definition of the ocean surface layer is composed of the set of buoyancy coordinates that ever reside at the ocean surface at a given horizontal position. The surface layer is found to be a physically distinct object with a diabatic and force balance that is largely isolated from the underlying adiabatic region in the interior. Within the ICC surface layer, the TWA meridional velocity is southward/northward in the top/bottom half and has a value near zero at the bottom. In the top half of the surface layer, the zonal forces due to wind stress and meridional advection of potential vorticity act to accelerate the TWA zonal velocity; equilibrium is obtained by eddies decelerating the zonal flow via a downward flux of eastward momentum that increases with depth. In the bottom half of the surface layer, the accelerating force of the wind stress is balanced by the eddy force and meridional advection of potential vorticity. The bottom of the surface layer coincides with the location where the zonal eddy force, meridional advection of potential vorticity, and zonal wind stress force are all zero. The net meridional transport S f within the surface layer is a small residual of its southward and northward TWA meridional flows. The mean meridional gradient of the surface layer buoyancy is advected by S f to balance the surface buoyancy flux.

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