Numerical simulations of Rossby-Haurwitz waves

Simulations of Rossby-Haurwitz waves have been carried out using four diffe rent high-resolution numerical shallow water models: a spectral model, two semi-Langrangian models predicting wind components and potential vorticity respectively, and a finite-volume model on a hexagonal-icosahedral grid. Th e simulations show that (i) unlike the nondivergent case, the shallow water Rossby-Haurwitz wave locally generates small-scale features and so has a p otential enstrophy cascade, and (ii) contrary to common belief, the zonal w avenumber 4 Rossby-Haurwitz wave is dynamically unstable and will eventuall y break down if initially perturbed. Implications of these results for the use of the Rossby-Haurwitz wave as a numerical model test case are discusse d. The four models tested give very similar results, giving confidence in t he accuracy and robustness of the results. The most noticeable difference b etween the models is that truncation errors in the hexagonal-icosahedral gr id model excite the Rossby-Haurwitz wave instability, causing the wave to b reak down quickly, whereas for the other models in the configurations teste d the instability is excited only by roundoff error at worst, and the Rossb y-Haurwitz wave breaks down much more slowly or nor at all.