13.7 PASS:
Rossby–Haurwitz wave

Author
 Stéphane Popinet
 Command
 sh rossby.sh rossby.gfs
 Version
 120530
 Required files
 rossby.gfs (view) (download)
rossby.sh ehp.gfv ehm.gfv h.gfv href.gfv ec6 eh4.ref eh5.ref eh6.ref
 Running time
 15 minutes 54 seconds
Rossby–Haurwitz waves are analytic solutions of the nonlinear
barotropic vorticity equation on the sphere. The parameters for this
test case are those proposed by Williamson et al
[47].
Figure 184: Detail of height field after one complete revolution
(24 days). Numerical solution in red and reference solution in
green. (a) C16, (b) C32, (c) C64. 
Figure 185: Detail of relative error field after one
complete revolution (24 days). Red is positive and green
negative. 10 metres contour interval. (a) C16, (b) C32, (c) C64. 
Figure 186: Evolution of maximum relative error on height with time. 
Figure 187: Convergence of final errors with spatial resolution. 
Figure 188: Evolution of kinetic energy with time. 
13.7.1 PASS:
Rossby–Haurwitz wave with a free surface

Author
 Stéphane Popinet
 Command
 sh ../rossby.sh ocean.gfs
 Version
 120614
 Required files
 ocean.gfs (view) (download)
ehp.gfv ehm.gfv h.gfv href.gfv ec6 eh4.ref eh5.ref eh6.ref
 Running time
 9 minutes 13 seconds
Same test case but using the GfsOcean solver implementing an
implicit solution to the linearised shallowwater equations.
The initial transient (geostrophic adjustement) seems to be too
strong.
Figure 189: Detail of height field after one complete revolution
(24 days). Numerical solution in red and reference solution in
green. (a) C16, (b) C32, (c) C64. 
Figure 190: Detail of relative error field after one
complete revolution (24 days). Red is positive and green
negative. 10 metres contour interval. (a) C16, (b) C32, (c) C64. 
Figure 191: Evolution of maximum relative error on height with time. 
Figure 192: Convergence of final errors with spatial resolution. 
Figure 193: Evolution of kinetic energy with time. 
13.7.2 PASS:
Rossby–Haurwitz wave with SaintVenant

Author
 Stéphane Popinet
 Command
 sh ../rossby.sh river.gfs
 Version
 120812
 Required files
 river.gfs (view) (download)
ehp.gfv ehm.gfv h.gfv href.gfv ec6 eh4.ref eh5.ref eh6.ref
 Running time
 18 minutes 15 seconds
Same test case but using the SaintVenant solver.
Figure 194: Detail of height field after one complete revolution
(24 days). Numerical solution in red and reference solution in
green. (a) C16, (b) C32, (c) C64. 
Figure 195: Detail of relative error field after one
complete revolution (24 days). Red is positive and green
negative. 10 metres contour interval. (a) C16, (b) C32, (c) C64. 
Figure 196: Evolution of maximum relative error on height with time. 
Figure 197: Convergence of final errors with spatial resolution. 
Figure 198: Evolution of kinetic energy with time. 