Large parts of the Earth's Atmosphere and Ocean have a gravitationally stable density stratification, with lighter fluid above heavier fluid. This stable stratification, combined with the planetary rotation, causes the most energetic motion to occur approximately in horizontal planes. For this situation we solve an approximate set of equations, called the Quasi-Geostrophic equations, using a fully implicit multigrid algorithm. In solutions for the decay from random initial conditions, we see the spontaneous emergence of concentrated vortices that regulate the evolution of the flow. The inclusion of the "beta effect", i.e., the variation in the Coriolis force with latitude due the Earth's sphericity, introduces Rossby waves and jets which compete with the vortices.