From the standpoint of tracer mixing, the natural set of coordinates are those defined with respect to the isopycnal or neutral directions. These coordinates define what is termed here the orthonormal isopycnal frame. Diffusion in this frame is assumed to be diagonal in the formulation of Redi (1982). The along isopycnal diffusion is on the order of 107 times greater than the diapycnal diffusion. Refer to Redi (1982), McDougall (1987), Gent and McWilliams (1990) for discussions motivating such diffusive mixing.
This section presents some technical details related to representing the isopycnal diffusion tensor, which is diagonal and thus simple in the orthogonal isopycnal frame, in the Eulerian (x,y,z)frame which is relevant for MOM. Some of these results are derived by Redi (1982) but using a different formalism.