Parallel Computation of Quasigeostrophic Flow Over a Sphere Using Spectral Methods on Coupled Layers

The goal of this thesis is to model and efficiently compute the evolution of atmospheric synoptic-scale cyclones and oceanic mesoscale eddies. This thesis consists of chapters (1) general fluid equations, (2) a derivation of a well suited model called the quasigeostrophic model, and (3) computation of the quasigeostrophic model. Because a general theory is desired before specializing, the first chapter concerns general fluid dynamics models - systems of partial differential equations coupling velocity, density, pressure, and temperature. General models will be derived through physical laws for conservation of mass, momentum, and energy. This model will be generalized to a rotating basis and transformed to spherical coordinates. Because the general equations are computationally expensive, chapter two is a derivation of an approximation called the quasigeostrophic model, which supports desired cyclone and eddy behavior. This derivation entails a formal scale analysis. The third chapter is devoted to computation of the quasigeostrophic model. The vertical coordinate will be discretized into layers. Each layer will be computed separately using spectral methods. Then each layer will be coupled with its neighboring layers. This process will be stepped forward in time. Although similar models have been computed before, the author's contribution is computing each layer in parallel, offering a computational speed-up. This model may be of interest to anyone modeling fluid dynamics on a planet or even a star. Although the author's primary motivation is Earth's cyclones and eddies.