The Earth's atmosphere and ocean are continuously in motion. Our research involves modelling such motions using the equations of fluid dynamics. Familiar examples are winds at the Earth's surface, and the rise and fall of the ocean surface (perhaps as wind-generated water waves with a time-scale of a few seconds, or as tides with a time-scale of 12 hours or more). However, all sorts of other motions occur throughout the depths of the atmosphere and ocean, some of which can be observed from satellites or with other modern technology. These motions interact with one another in a complicated way, helping to determine the climate of the atmosphere-ocean system. The emphasis is on developing relatively simple systems of equations, retaining only those physical processes which are necessary to describe the phenomenon. This approach lends itself to mathematical analysis, and has a rich history featuring distinguished scientists such as Laplace, Lord Rayleigh and Lord Kelvin. However, the classical approach is now complemented by the use of numerical solutions of less idealised situations, or complicated nonlinear or turbulent flows.