Subsections

# Horizontal/Vertical 2nd Order Tracer Diffusive Operators

### In z-coordinates

In -coordinates, the horizontal/vertical second order tracer diffusion operator is given by:
 (B.1)

### In generalized vertical coordinates

In -coordinates, we defined the slopes of -surfaces, and by (A.1) and the vertical/horizontal ratio of diffusion coefficient by . The diffusion operator is given by:

 where (B.2)

or in expanded form:

Equation (B.2) is obtained from (B.1) without any additional assumption. Indeed, for the special case and thus , we introduce an arbitrary vertical coordinate as in Appendix A and use (A.1) and (A.2). Since no cross horizontal derivative appears in (B.1), the (,) and (,) planes are independent. The derivation can then be demonstrated for the (, (,) transformation without any loss of generality:

Gurvan Madec and the NEMO Team
NEMO European Consortium2017-02-17