Fluid mechanics plays a role of enormous importance in everyday life - in the world around us, and even inside our own body. The variety of fluid-dynamical phenomena is almost endless.

Fluid flow is governed by a complicated nonlinear system of partial differential equations. In many situations of interest the flow spans a huge range of length scales, with the nonlinearity of the governing equations resulting in the transfer of energy from one length scale to another. Because of this complexity, the field of fluid mechanics has been the birth place of many important fields in mathematics. It has stimulated much work in areas such as partial differential equations, asymptotics and perturbation theory, computational methods, nonlinear waves, including solitons, instability theory, chaos, and stochastic processes. Despite these developments, turbulence in fluids remains one of the major unsolved problems in classical physics. In general, the research projects within each of these themes are characterized by a combination of theoretical modelling, numerical simulations and laboratory experiments.

Indeed, within the field of fluid mechanics there is something for students of all interests. For example, one of the forthcoming graduate courses, Environmental and Geophysical Fluid Dynamics, is primarily concerned with fluid flow in rivers, lakes, oceans and the atmosphere. Such flows dominate our physical existence. Geophysical Fluid Dynamics (GFD) is traditionally the study of naturally occurring large scale fluid motions in the oceans and in the atmosphere which are affected by the Earth's rotation, but also includes extraterrestrial atmospheres and the interior of the gas giants such as Jupiter. Examples of large scale motions are the Gulf Stream in the North Atlantic Ocean and atmospheric blocking events, one of which was responsible for the great heat wave in Europe in 2003. Over the past 30 years attention has been increasingly focused on the impact of large scale fluid flows on the environment, highlighted by fundamental issues such as global warming and long-term climate change. Smaller scale motions, such as turbulence and mixing caused by internal waves, and surface water waves have a direct impact on bio-geochemical processes in oceans and lakes and on hence on human activity. Due to their ubiquitous nature, these motions are also of fundamental importance to the large scale circulation in both the oceans and atmosphere.