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Ocean Science An interactive open-access journal of the European Geosciences Union
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Volume 2, issue 2
Ocean Sci., 2, 161–171, 2006
https://doi.org/10.5194/os-2-161-2006
© Author(s) 2006. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
Ocean Sci., 2, 161–171, 2006
https://doi.org/10.5194/os-2-161-2006
© Author(s) 2006. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  12 Oct 2006

12 Oct 2006

Energetics of the layer-thickness form drag based on an integral identity

H. Aiki1 and T. Yamagata1,2 H. Aiki and T. Yamagata
  • 1Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama-city 236-0001, Japan
  • 2Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Tokyo 113-0033, Japan

Abstract. The vertical redistribution of the geostrophic momentum by the residual effects of pressure perturbations (called the layer-thickness form drag) is investigated using thickness-weighted temporal-averaged mean primitive equations for a continuously stratified fluid in an adiabatic formulation. A four-box energy diagram, in which the mean and eddy kinetic energies are defined by the thickness-weighted mean velocity and the deviation from it, respectively, shows that the layer-thickness form drag reduces the mean kinetic energy and endows the eddy field with an energy cascade. The energy equations are derived using an identity (called the "pile-up rule") between cumulative sums of the Eulerian mean quantity and the thickness-weighted mean quantity in each vertical column. The pile-up rule shows that the thickness-weighted mean velocity satisfies a no-normal-flow boundary condition at the top and bottom of the ocean, which enables the volume budget of pressure flux divergence in the energy diagram to be determined. With the pile-up rule, the total kinetic energy based on the Eulerian mean can be rewritten in a thickness-weighted form. The four-box energy diagram in the present study should be consistent with energy diagrams of layer models, the temporal-residual-mean theory, and Iwasaki's atmospheric theory. Under certain assumptions, the work of the layer-thickness form drag in the global ocean circulation is suggested to be comparable to the work done by the wind forcing.

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