Advanced Ocean Modelling: Using Open-Source Software

34 3 Basics of Nonhydrostatic ModellingFig. 3.9 Exercise 3. Ensemble of vertical profiles (thin lines) of dynamic pressure, divided by ρ o g,taken from the entire model domain after 100 secs of iteration. The thick line shows the theoreticalresult of maximum pressure values according to Eq. (3.12)Total water depth can be changed by variation of either vertical grid spacing orthe total number of vertical levels nz in the declaration section. The author recommendsthe second option knowing that a coarser vertical resolution can act as a filterbiasing the true dynamics of the process.3.5.5 Implementation of Variable Bottom TopographyThe aim is to test the vertical ocean-slice model for variable bottom topography,such as that shown in Fig. 3.10. To this end, two logical pointer arrays are declaredas to indicate whether a grid cell is “dry” or “wet”. Pointer values are specified atpressure grid points.Zero-gradient conditions for dynamic pressure need to be implemented at allsolid surfaces. This is done implicitly by setting the respective coefficients inthe Poisson equation (Eq. 3.27) to zero and by performing the S.O.R. iterationexclusively in wet grid cells. Note that calculation of new velocity components isrestricted to wet grid points excluding those defining a solid surface (see Fig. 3.3).The folder “Miscellaneous/Exercise 3 Variation” on the book’s ftp site contains themodified model code.Fig. 3.10 A simple bathymetry for tests of the vertical ocean-slice model