Advanced Ocean Modelling: Using Open-Source Software

3.2 2D Vertical-Slice Modelling 23Fig. 3.2 The two-dimensional vertical ocean sliceThe continuity equation (Eq. 1.2) can be written as:∂u∂x + ∂w∂z = 0 (3.2)3.2.2 The Arakawa C-GridFigure 3.3 shows the configuration of the Arakawa C-grid (Arakawa and Lamb, 1977)applied to the vertical ocean slice. This grid is the basis for all exercises of this book.Vertical location is defined by the level index i and vertical grid spacing Δz. Theuppermost grid cell carries the index i = 1, whereas i = nz points to the bottomlayer. Grid points for pressure and other scalars (i.e. density) are centred betweenu- and w-velocity grid points. The undisturbed sea surface is aligned with verticalvelocity grid points of uppermost grid cells.Fig. 3.3 Arakawa C-grid for a vertical ocean slice