A Finite-Mode Model of Ideal Fluid Dynamics on the 2-Sphere

We develop the finite-mode model for a two-dimensional Euler system on the sphere based on Hopped’s discovery in group theory. This model strives to keep as many invariants of the original Euler equation as possible. Theoretically, the number of invariants in this model is limited only by computing power. At present, almost all the popular numerical models in weather and climate researches such as numerical weather prediction models and general circulation models (GCMs) use spectral method. However all these spectrally truncated models do not keep all the invariants except for the energy and the enstrophy. By using this model one is able to study the influence from some other lost invariants. The result from this model is expected to be closer to that of the original Euler equations than from ordinary spectrally truncated models. The relevant fundamental equations and important formulas for this model are given explicitly.