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10.2  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 45 seconds

A simulation is initialised with an exact solution found by Lamb [15] 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 95 illustrates the solution obtained after three wave periods.

Following [6], 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 [6], because the timestep used is much larger. The time-explicit codes tested in [6] have stronger stability requirements than Gerris.


Figure 95: 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

10.2.1  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
1 minutes 45 seconds

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

Figure 96 illustrates the solution obtained after three wave periods.


Figure 96: 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
50.92242.5
60.9980.5
70.99850.3


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