5.3 Exercise 20: Geostrophic Adjustment in 3D
131
It can be shown (Kowalik and Murty, 1999) that the CLF stability associated with
the propagation of surface gravity waves is given by:
Δt ≤
min (Δx, Δy)
√
2gh max
(5.14)
where h max is the maximum water depth of the model domain. Notice that the
factor of two appears here in the denominator. The latter condition is relevant
for applications considering a free sea surface. Longer numerical time steps may
work with choice of the rigid-lid approximation (see Sect. 3.7). In principle, the
three-dimensional free-surface hydrodynamic level model, described here, can be
employed to simulate any of the previous exercises in three-dimensional space.
Nevertheless, to avoid super-long simulation times, the reader should keep the number of grid points as small as possible. Also data output should be restricted to
a few selected horizontal and vertical transects of variables to avoid data-storage
problems.
5.3 Exercise 20: Geostrophic Adjustment in 3D
5.3.1 Aim
The aim of this exercise is to test and validate the three-dimensional free-surface
hydrodynamic level model by means of the geostrophic adjustment problem using
a configuration similar to that of Exercise 15.
5.3.2 Task Description
The model domain is 5×5 km in lateral extent and 500 m in depth (Fig. 5.3). Lateral
grid 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 the
number of grid points used in previous model simulations. Zero-gradient conditions
are used for all variables at lateral boundaries.
Fig. 5.3 Initial configuration for Exercise 20
131
It can be shown (Kowalik and Murty, 1999) that the CLF stability associated with
the propagation of surface gravity waves is given by:
Δt ≤
min (Δx, Δy)
√
2gh max
(5.14)
where h max is the maximum water depth of the model domain. Notice that the
factor of two appears here in the denominator. The latter condition is relevant
for applications considering a free sea surface. Longer numerical time steps may
work with choice of the rigid-lid approximation (see Sect. 3.7). In principle, the
three-dimensional free-surface hydrodynamic level model, described here, can be
employed to simulate any of the previous exercises in three-dimensional space.
Nevertheless, to avoid super-long simulation times, the reader should keep the number of grid points as small as possible. Also data output should be restricted to
a few selected horizontal and vertical transects of variables to avoid data-storage
problems.
5.3 Exercise 20: Geostrophic Adjustment in 3D
5.3.1 Aim
The aim of this exercise is to test and validate the three-dimensional free-surface
hydrodynamic level model by means of the geostrophic adjustment problem using
a configuration similar to that of Exercise 15.
5.3.2 Task Description
The model domain is 5×5 km in lateral extent and 500 m in depth (Fig. 5.3). Lateral
grid 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 the
number of grid points used in previous model simulations. Zero-gradient conditions
are used for all variables at lateral boundaries.
Fig. 5.3 Initial configuration for Exercise 20