Conservation Properties of the Hamiltonian Particle-Mesh method for the Quasi-Geostrophic Equations on a sphere

The Hamiltonian particle-mesh (HPM) method is used to solve the Quasi-Geostrophic model generalized to a sphere, us-ing the Spherepack modeling package to solve the Helmholtz equation on a colatitude-longitude grid with spherical harmon-ics. The predicted energy conservation of a Poisson system is shown to be approximately retained and statistical mean-field theory is verified. Acknowledgements I would like to start with thanking my supervisor Jason Frank for introducing me to the perfect cocktail of numerics, statistics and computational fluid dynamics. His guidance, inspiration and enthusiasm made this thesis work possible. Special thanks are due to Keith for his company as well as constructive comments and suggestions throughout the whole process and at the final stages. Thanks also to Janis and Jannis for helpful discussions, and the MAC1 team, Daan, Jesse, Sergiy and Wander. I would also like to thank my family for their support, especially my father for reminding me from time to time how to handle this process in a calm, cool and collected way. Last but not least, thanks to Aziz for being there for me through it all. Contents