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6.1  "Garden sprinkler effect" in wave model

Author
Stéphane Popinet
Command
sh garden.sh
Version
1.2.1
Required files
garden.gfs (view) (download)
garden.sh end.gfv mesh.gfv
Running time
41 minutes

The wave model is used to reproduce the classical "Garden Sprinkler Effect" (GSE), a numerical artifact of the discrete directions of wave propagation (see Tolman, 2002).

A spatially-Gaussian wave spectrum is initialised in a 5000 km-squared domain. The other parameters are those of Tolman, 2002.

The final (t = 5 days) significant wave height for different model runs is illustrated in Figure 48. The interval between the isolines is 0.1 metres as in Figure 1 of Tolman, 2002. For a small number of discrete directions (24), the GSE is evident and the results closely match those of Tolman both for the constant resolution and the adaptive version of the code. For larger number of directions (60 and 120), the results do not show any obvious GSE and match the corresponding results of Tolman (Figure 1.b of Tolman, 2002 but note that the spatial resolution of Tolman is finer, 25 km rather than 78 km here).


Figure 48: Final (t = 5 days) significant wave height for different model runs.

The evolution in time of the significant wave height together with the corresponding adaptive discretisation is illustrated in Figure 49 for 120 directions. The mesh is adapted according to the spatial gradient in the significant wave height. This results in substantial savings in computational cost as illustrated by the timings given in Table 1. The computational cost with 120 directions is comparable to the cost with 24 directions on a regular (i.e. non-adaptive) mesh. This demonstrates that the GSE can be alleviated – at comparable computational cost – by combining adaptive refinement with a refined discretisation in direction space.


Figure 49: Evolution of the significant wave height and adaptive mesh. 120 directions.


Table 1: CPU time for the four models of Figure 48.
Adaptivity# directionsCPU time (seconds)
No24582
Yes24179
Yes60312
Yes120699


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