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11.3  PASS: Coastally-trapped waves

Author
Stéphane Popinet
Command
sh waves.sh waves.gfs
Version
100323
Required files
waves.gfs (view) (download)
waves.sh solution.gfv correlation.ref
Running time
2 minutes 1 seconds

A simulation is initialised with an exact solution found by Lamb [23] for inertia-gravity waves in a circular, flat-bottomed basin on an f-plane.

The waves should rotate unchanged around the basin. This is a good test of the shallow-water solver with Coriolis terms and non-trivial coastlines.

Figure 135 illustrates the solution obtained after three wave periods.

Following [11], Table 13 presents the phase error and the maximum correlation between the computed solution and the exact solution. Note that these results are not directly comparable to [11], because the timestep used is much larger. The time-explicit codes tested in [11] have stronger stability requirements than Gerris.


Figure 135: Surface-height after a rotation of 3 wave periods for a resolution of 9.375 km.


Table 13: Maximum correlation and phase error as functions of resolution.
LevelMaximum CAngle of max C
50.92532.4
610.1
710

11.3.1  PASS: Coastally-trapped waves with adaptive refinement

Author
Stéphane Popinet
Command
sh ../waves.sh adaptive.gfs
Version
100323
Required files
adaptive.gfs (view) (download)
solution.gfv correlation.ref
Running time
59 seconds

Same test case as before but with adaptive refinement (using the vorticity criterion).

Figure 136 illustrates the solution obtained after three wave periods.


Figure 136: Surface-height after a rotation of 3 wave periods. The maximum resolution is 9.375 km (dark red), the minimum resolution is 150 km (dark blue).


Table 14: Maximum correlation and phase error as functions of resolution.
LevelMaximum CAngle of max C
50.92212.6
60.99810.7
70.99850.3


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