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Momentum Balance of the Wind-Driven and Meridional Overturning Circulation

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  • 1 Department of Physics, University of Oxford, Oxford, United Kingdom
  • | 2 Department of Earth Sciences, University of Oxford, Oxford, United Kingdom
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Abstract

When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a “rotational force” in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces that are confined to the basin boundaries and drive the overturning circulation. Potential applications of the approach to diagnosing the output of ocean circulation models, alternative and more accurate formulations of numerical ocean models, the dynamics of boundary layer separation, and eddy forcing of the large-scale ocean circulation are discussed.

Corresponding author address: Dr. David P. Marshall, Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom. E-mail: marshall@atm.ox.ac.uk

Abstract

When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a “rotational force” in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces that are confined to the basin boundaries and drive the overturning circulation. Potential applications of the approach to diagnosing the output of ocean circulation models, alternative and more accurate formulations of numerical ocean models, the dynamics of boundary layer separation, and eddy forcing of the large-scale ocean circulation are discussed.

Corresponding author address: Dr. David P. Marshall, Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom. E-mail: marshall@atm.ox.ac.uk
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