Non-uniform adaptive vertical grids for 3D numerical ocean models

A new strategy for the vertical gridding in terrain-following 3D ocean models is presented here. The vertical grid adaptivity is partially given by a vertical diffusion equation for the vertical layer positions, with diffusivities being proportional to shear, stratification and distance from the boundaries. In the horizontal, the grid can be smoothed with respect to z-levels, grid layer slope and density. Lagrangian tendency of the grid movement is supported. The adaptive terrain-following grid can be set to be an Eulerian-Lagrangian grid, a hybrid σ-ρ or σ-z grid and combinations of these with great flexibility. With this, internal flow structures such as thermoclines can be well resolved and followed by the grid. A set of idealised examples is presented in the paper, which show that the introduced adaptive grid strategy reduces pressure gradient errors and numerical mixing significantly. The grid adaption strategy is easy to implement in various types of terrain-following ocean models. The idealised examples give evidence that the adaptive grids can improve realistic, long-term simulations of stratified seas while keeping the advantages of terrain-following coordinates.