Reevaluation of the Takano–Oonishi Scheme for Momentum Advection on Bottom Relief in Ocean Models

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Abstract
In the Takano and Oonishi models the finite-difference analog of the nonlinear momentum advection contains the concept of diagonally upward/downward mass and momentum fluxes along the bottom slope, and the generalized Arakawa scheme for the horizontal advection, modified to be fit to arbitrary coastal shape. It has been said to have a good performance, but is not widely used, largely because of its complicated expression. The purpose of this paper is to reevaluate the Takano–Oonishi scheme for the momentum advection to put it to more practical use by using the redefinition of it in a simple, generalized form and the confirmation of its good performance through a comparison with other schemes. Based on the definition of mass continuity for a momentum cell (U cell) in terms of that for tracer cells (T cell), the vertical and horizontal mass and momentum fluxes for the U cell are generalized on arbitrary bottom relief in simple forms. Although the grid spacing of the present model is different from that of the Geophysical Fluid Dynamics Laboratory model, applicability of the present scheme to the latter grid spacing is discussed. Then, the present scheme is tested in an eddy-resolving ocean model and its results are compared with those of a traditional scheme. The present scheme shows good performance in computational efficiency as well as reality of the simulated flow field.

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