Vortex erosion and amalgamation in a new model of large scale flow on the sphere

The pseudo-spectral methodology that is typically employed to simulate fluid flow in spherical geometry exhibits, among other limitations, a severe degradation of performance at high resolution. Finite element models based upon the application of multigrid methods may be designed so as to avoid this defect while also allowing for greater local control over the computational mesh. We describe herein the details of the mathematical methods that are required to implement such a computational structure and apply these methods to design a model based upon the two dimensional spherical barotropic vorticity equation, the simplest framework within which their viability may be tested. The model is thereafter employed in the analysis of two essentially inviscid nonlinear dynamical problems in order to provide proof of concept. The first of these test problems entails repeating a well known pseudospectral calculation of the erosion of a polar vortex under slow, quasi-steady, Rossby wave forcing at low zonal wavenumber. The second test problem concerns the simulation of the nonlinear development of the instability of a zonal shear band into a train of like signed vortices which subsequently amalgamate through the nonlinear pairing interaction. Results of these test calculations, as well as those based upon additional analyses that we discuss herein, demonstrate that the performance of our initial methodology meets the basic criteria of fluid flow simulation. This suggests, on the basis of theoretical efficiency, that optimized versions could eventually compete with the large production codes which are in operation today. Our future intent is to further develop this computational structure so as to create a new class of three-dimensional general circulation models that may be employed in a wide variety of astrophysical and atmosphere-ocean applications. 25 refs., 11 figs