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Estimating Lorenz’s Reference State in an Ocean with a Nonlinear Equation of State for Seawater

Estimating Lorenz’s Reference State in an Ocean with a Nonlinear Equation of State for Seawater
Estimating Lorenz’s Reference State in an Ocean with a Nonlinear Equation of State for Seawater
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.
Circulation/Dynamics, Buoyancy, Forcing, Ocean circulation
0022-3670
1242-1257
Saenz, Juan A.
e8ee1f95-71ce-4915-af13-b8c2b7f591ae
Tailleux, Rémi
a2bad901-79fb-42ef-9633-7f2135c0f930
Butler, Edward D.
8b825043-cd28-4c62-ac38-46d662accebf
Hughes, Graham O.
f01cfd00-6286-4daf-9ef9-ec0d0f5c762b
Oliver, Kevin I.C.
588b11c6-4d0c-4c59-94e2-255688474987
Saenz, Juan A.
e8ee1f95-71ce-4915-af13-b8c2b7f591ae
Tailleux, Rémi
a2bad901-79fb-42ef-9633-7f2135c0f930
Butler, Edward D.
8b825043-cd28-4c62-ac38-46d662accebf
Hughes, Graham O.
f01cfd00-6286-4daf-9ef9-ec0d0f5c762b
Oliver, Kevin I.C.
588b11c6-4d0c-4c59-94e2-255688474987

Saenz, Juan A., Tailleux, Rémi, Butler, Edward D., Hughes, Graham O. and Oliver, Kevin I.C. (2015) Estimating Lorenz’s Reference State in an Ocean with a Nonlinear Equation of State for Seawater. Journal of Physical Oceanography, 45 (5), 1242-1257. (doi:10.1175/JPO-D-14-0105.1).

Record type: Article

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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e-pub ahead of print date: 12 May 2015
Keywords: Circulation/Dynamics, Buoyancy, Forcing, Ocean circulation
Organisations: Physical Oceanography

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Local EPrints ID: 377987
URI: http://eprints.soton.ac.uk/id/eprint/377987
ISSN: 0022-3670
PURE UUID: 3c5e9039-6a7b-49ff-9318-e9ce352d6d58

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Date deposited: 12 Jun 2015 10:54
Last modified: 14 Mar 2024 20:14

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Contributors

Author: Juan A. Saenz
Author: Rémi Tailleux
Author: Edward D. Butler
Author: Graham O. Hughes

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