The problem as posed is inviscid. Although most models will occasionally require finite values of viscosity for numerical reasons, SEOM was successfully run on this non-turbulent problem with zero explicit viscosity. Figure 2 shows the typical behavior of the soliton. Shortly after initiation, the Rossby soliton sheds an eastward-propagating equatorial Kelvin wave as it adjusts from its initial state and begins to propagate westward. During this initial adjustment, the soliton loses approximately 7% of its initial amplitude. Note that the initial state of the model is inexact both because of finite numerical resolution and because the analytical solution is itself approximate.
For the ``standard'' run, the average resolution of 0.5 was achieved by using (eighth order) elements. It can also be achieved by using (fourth order) elements. Higher and lower resolutions were also tried, as shown in figure 3 and table 3.
The solutions show that for the same resolution, the higher-order scheme does a better job of representing the Rossby soliton. Anything less than a resolution of 0.5 will be inadequate to achieve an accurate result. This provides between two and three points in one e-folding scale for the exponential in y. For the under-resolved cases, the animations show that the maximum amplitude oscillates, as does the distance between the two maxima. Initializing with the first-order solution reduces the magnitude of the initial Kelvin wave propogating to the east, at least in the well-resolved cases (run_f.gif), but otherwise produces similar results.