| Volumes and Issues Contents of Issue 2 |
www.ocean-sci.net/2/161/2006/
doi:10.5194/os-2-161-2006
© Author(s) 2006. This work is licensed
under a Creative Commons License.
Energetics of the layer-thickness form drag based on an integral identity
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.
Final Revised Paper (PDF, 430 KB) Discussion Paper (OSD)
Citation: Aiki, H. and Yamagata, T.: Energetics of the layer-thickness form drag based on an integral identity, Ocean Sci., 2, 161-171, doi:10.5194/os-2-161-2006, 2006. Bibtex EndNote Reference Manager XML
