Chapter 13 - Geophysical Fluid Dynamics

Abstract

This chapter concerns mathematical modelling of large-scale fluid flows relative to a rotating frame of reference, for which the effects of rotation are dominant and to leading order there is a balance of horizontal pressure gradients and Coriolis forces. The principal application is to oceanic and atmospheric flows with horizontal scales of tens of kilometres or more, and timescales of days or more. A fundamental equation in the dynamics of such flows is that for quasigeostrophic potential vorticity, and this is derived in the first part of the chapter, with stratification effects included in the form of layers with constant density within each layer. Large-scale wave-like behaviour is supported in the form of Rossby waves, and some basic properties of these waves are presented. Simplified conceptual quasigeostrophic models provide understanding of dynamical processes, and two examples are described: ocean spin-up and multiple equilibria.