Advanced Ocean Modelling: Using Open-Source Software

5.3 Exercise 20: Geostrophic Adjustment in 3D 131It can be shown (Kowalik and Murty, 1999) that the CLF stability associated withthe propagation of surface gravity waves is given by:Δt ≤min (Δx, Δy)√2ghmax(5.14)where h max is the maximum water depth of the model domain. Notice that thefactor of two appears here in the denominator. The latter condition is relevantfor applications considering a free sea surface. Longer numerical time steps maywork with choice of the rigid-lid approximation (see Sect. 3.7). In principle, thethree-dimensional free-surface hydrodynamic level model, described here, can beemployed to simulate any of the previous exercises in three-dimensional space.Nevertheless, to avoid super-long simulation times, the reader should keep the numberof grid points as small as possible. Also data output should be restricted toa few selected horizontal and vertical transects of variables to avoid data-storageproblems.5.3 Exercise 20: Geostrophic Adjustment in 3D5.3.1 AimThe aim of this exercise is to test and validate the three-dimensional free-surfacehydrodynamic level model by means of the geostrophic adjustment problem usinga configuration similar to that of Exercise 15.5.3.2 Task DescriptionThe model domain is 5×5 km in lateral extent and 500 m in depth (Fig. 5.3). Lateralgrid spacings are set to Δx = Δy = 2 km. The vertical grid spacing is set to Δz =20 m. This gives a total of 25×25×25 =15,625 grid points, which exceeds by far thenumber of grid points used in previous model simulations. Zero-gradient conditionsare used for all variables at lateral boundaries.Fig. 5.3 Initial configuration for Exercise 20