Isoneutral Diffusion in a strongzstrong-Coordinate Ocean Model.pdf

MAY 1998 G R I F F I E S E T A L . 805 Isoneutral Diffusion in a z-Coordinate Ocean Model STEPHEN M. GRIFFIES Geophysical Fluid Dynamics Laboratory, Princeton University, Princeton, New Jersey ANAND GNANADESIKAN Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, New Jersey RONALD C. PACANOWSKI Geophysical Fluid Dynamics Laboratory, Princeton University, Princeton, New Jersey VITALY D. LARICHEV Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, New Jersey JOHN K. DUKOWICZ AND RICHARD D. SMITH Los Alamos National Laboratory, Theoretical Division, Los Alamos, New Mexico (Manuscript received 3 March 1997, in final form 6 August 1997) ABSTRACT This paper considers the requirements that must be satisfied in order to provide a stable and physically based isoneutral tracer diffusion scheme in a z-coordinate ocean model. Two properties are emphasized: 1) downgradient orientation of the diffusive fluxes along the neutral directions and 2) zero isoneutral diffusive flux of locally referenced potential density. It is shown that the Cox diffusion scheme does not respect either of these properties, which provides an explanation for the necessity to add a nontrivial background horizon