New spectral methods for fluid dynamical applications on the sphere

Simulations of many large-scale geophysical systems, such as climate, mantle convection and magnetic field generation in the core require computations in a spherical geometry. Traditional computer models are relatively slow because the spatial dependence of relevant physical variables (e.g. temperature) at fixed radius are represented by somewhat complicated mathematical functions, the so-called 'spherical harmonics'. A new, simpler representation has been found in a new coordinate system and this work is concerned with exploiting this representation in the development of new computationally efficient methods for simulating these systems in a spherical geometry