43. Isoneutral diffusion discretization

The purpose of this appendix is to present a full derivation of MOM's isoneutral diffusion discretization. Most readers will find this appendix quite uninteresting. It is presented as part of the MOM manual, nevertheless, since it illustrates in the utility of functional approaches to deriving discretizations. A more streamlined, and hopefully interesting, discussion can be found in Griffies, Gnanadesikan, Pacanowski, Larichev, Dukowicz, and Smith (hereafter, Griffies et al. 1998).

Brief history of this appendix:

• Early 1996: Derivation presented for full bottom cells.
• June 1997: Generalization to partial bottom cells.
• March 1998: Typos corrected in the discussion of the meridional flux. These mistakes were not made in the original MOM 2 code.
• May 1999: Bug found in computation of vertical flux component for partial cells. Division by dht should have been division by dhwt. Code and manual updated.

Note that in this Appendix, diagonal diffusive fluxes are considered positive if they are down the tracer gradient. The code in MOM, however, employs the opposite convention. The diffusion operator in MOM picks up a minus sign which renders it the same as discussed in this Appendix. Clarification of this comment is provided in Section .