Numerical discretization of rotated diffusion operators in ocean models

A method to improve the behavior of the numerical discretization of a rotat ed diffusion operator such as, for example, the isopycnal diffusion paramet erization used in large-scale ocean models based on the so-called z-coordin ate system is presented. The authors then focus exclusively on the dynamica lly passive tracers and analyze some different approaches to the numerical discretization. Monotonic schemes are designed but are found to be rather c omplex, while simpler, linear schemes are shown to produce unphysical under shooting and overshooting. It is suggested that the choice of an appropriat e discretization method depends on the importance of the rotated diffusion in a given simulation, whether the field to be diffused is dynamically acti ve or not.