This paper presents a convergence study for second order finite difference Laplacian diffusion used in ocean models. For demonstration, ocean model simulations are performed over a rectangular domain, based on the North Pacific subtropical gyre region with grid resolution between 1/2¿ and 1/32¿ and with horizontal eddy viscosity coefficient (AH) ranging from 8000 to 30 m2 s-1. A range of AH which is appropriate for useful model simulations of an oceanic domain is found to exist. This range is determined by examining the spatial patterns of Eddy kinetic energy and mean sea surface height. The results fall into three broad categories: (a) converged, (b) converging, and (c) numerical problems. Solutions in the converged category do not change with increased grid resolution, and solutions in the numerical problems category exhibit distinct differences to the converged result at the same AH.