When acting on the active tracers, the isoneutral diffusion operator is nonlinear since the diffusion tensor is a function of the active tracers. This point is important since the functional formalism assumes the diffusion operator to be a linear self-adjoint operator. However, since it is assumed that the diffusion operator is the same for both the active and passive tracers, the restriction of the functional formalism to the passive tracers is no problem. What is done is to use the functional machinery assuming the tracer is passive. When it comes time to discretize the neutral directions, the understanding of how to properly align the slopes so that the diffusion operator is self-consistent (i.e., so that it will not flux locally referenced potential density along the neutral directions) will be incorporated. Without ensuring self-consistency, the variance reducing diffusion operator can produce an accumulation of active tracer variance at the grid scale, which can create a useless numerical solution full of grid noise.
Please see the postscript version of the MOM Manual, via anonymous ftp at ftp.gfdl.gov, for the remainder of this appendix.