Flow over topography and instability on beta-planes: the effects of different expansion representations

In our study, we use a truncation scheme and expansion of the streamfunction, in terms of a nonorthogonal large-scale flow -Uy and meridional sine expansions for both the zonal and wave terms. These results are compared with those in a model in which the perturbation has a purely orthogonal function representation. At severe truncation there are significant differences between the two. At high resolution, we find that in some parts of parameter space there are significant qualitative, as well as quantitative, differences between the models. The nonlinear stability properties of stationary flow in each model are also examined and differences even at infinite resolution are attributed to Gibbs phenomena with the purely orthogonal function representation. -from Authors