Reduced models for geophysical fluid dynamics

Abstract

This thesis present a self-consistent derivation of reduced fluid models for geophysical dynamics confined to the midlatitude region. The reduced model will be derived by use of a regular perturbation method, that gives the same result as the classical models, such as the barotropic and baroclinic quasi-gestrophic potential vorticity model. It will be shown that such a rigorous treatment self-consistently comprises otherwise classic assumptions known as, the Boussinesq approximation, shallow-water approximation, $\beta$-plane approximation (slab-approximation) and thin shell approximation. We use the understanding of these reduced models to generalize the baroclinic quasi-gestrophic potential vorticity model to include interaction with global scale. This will be done by using a multi-scale expansion, assosisert with the separation of spatio-temporal scales.