Influence of a step-like coastline on the basin scale vorticity budget of mid-latitude gyre models

摘要: Global vorticity budgets in C-grid shallow water (SW) and quasi-geostrophic (QG) models of winddriven ocean circulation with free-slip boundary conditions are considered. For both models, it is pointed out that the discretized equation defined only over a subdomain excludes grid nodes. At finite resolution, this implies an advective flux across perimeter domain. rectangular basins where axes aligned basin walls, tends to zero as resolution increased. We also consider case which rotated respect basin, so step-like coastline results. Increased then leads more steps and, because domain particularly large at steps, no longer obvious increased should reduce flux. Results found be sensitive numerical details. In particular, we different formulations for non-linear terms (for SW QG models) two viscous stress tensor model [the conventional five-point Laplacian δ–ζ suggested by Madec et al. (J. Phys. Oceanogr. 21, 1349–1371)]. model, overall behavior term dependent on formulation terms. The best combination enstrophy-preserving advection scheme. With combination, non-rotated recovered converge towards increasing resolution. poorest case, diverges some rotation angles crashes others. convergence order absolute near unity (roughly same model). Most error (especially high resolution) related errors β (which hidden contribution However, less especially when Jacobian proposed Arakawa Comput. 1, 119–143) used. DOI: 10.1034/j.1600-0870.2003.00015.x