Case 06. Rossby Equatorial Soliton
Case 6.Rossby Equatorial Soliton  


As implemented, the spatial order of accuracy of the advective fluxes in FVCOM is second order accurate. A loglog plot of the r.m.s. error versus spatial resolution for this test case shown in Figure 3 confirms this. Several error metrics are shown in Table 1 for various grid spacing. The values are comparable to the results obtained using 4th order elements in the SEOM code found here. At low spatial resolutions on the order of 10 elements/wavelength, the temporal energy loss is unacceptable. However, as the grid is refined to 20 and 40 elements/wavelength, this discrepancy can be quickly reduced to acceptable levels. Calculations for an updated test case incorporating a longer channel with periodic boundary conditions are currently underway. 



Discussion: As expected, the coarsest mesh was unable to resolve the wave form for more than one wave period (T=25). The decay of the maximum surface elevation was quite rapid, falling to less than 50% of the initial amplitude after only 40 time units. As the mesh density is increased, one can see that both the r.m.s. error and the defect in maximum surface amplitude decrease due to the increase in spatial resolution. The wave speed also converges towards the analytical solution as the mesh spacing approaches .125. Note that some error will always remain regardless of the mesh resolution due to the inconsistency between the zeroth order solution for the initial conditions and the governing equations used in the simulation. In Figure 3, a loglog plot of r.m.s. error vs. grid spacing is shown. The average slope of this line (1.83) can be correlated with the spatial order of accuracy. The animations provided compare the computed and analytical waveforms as they propagate to the west over a period of 40 time units. In the finer meshes, a spurious wave can be seen propagating to the east following the initial adjustment. This wave is also present in the SEOM results and may be eliminated by initializing with a higher order analytical solution. The error metrics from the FVCOM computations shown in Table 1 compare well with results computed using the highorder spectral element model SEOM. 



Description of Metrics Geoff Cowles 26/08/2003 